class plan for math 101...assignments will be returned only to the student who did them. (you can...
TRANSCRIPT
Class Plan for Math 101David B Sher
Office B3068
Phone 572-7383 ext 26830
Email davidbsher-fall12yahoocom
webpage httpwwwmatcmpnccedusherdclassdocmat101
Twitter Math4Sher - shermat101
Office Hours Tuesday 1-215 Wednesday 1100-1215
Text Logic and Set Theory with Applications 6th Edition by Cheifetz Avenoso etc
Topics
Introduction Section 51 2 hours
Connectives Section 52 3 hours
Diagrams Section 53 4 hours
Survey Problems Section 54 4 hours
Laws Section 55 5 hours
Probability Section 6364 3 hours
Set Theory
Language Section 11 1 hour
Connectives Section 12 1 hour
Truth Tables Section 1415 3 hours
Arguments Section 21313233 5 hours
Logic
Grading10 Quizzes 30 Reports (5) 60 Exams (3)
Expulsion (not absence) from Class 3 times is an F ndash Vandalism will result in an FDISABILITIES STATEMENTIf you have -- or suspect you have -- a physical psychological medical or learning disability that may have an impact on your ability to carry out the assigned coursework I urge you to contact the staff at the Center for Students With Disabilities Bldg U (behind the old College Union) 572-7241 TTY 572-7617 The counselors at CSD will review your concerns and determine with you what accommodations are necessary and appropriate All information and documentation will be kept confidentialPrerequisiteIf you were placed in remedial math (math001 or math002) and have not passed math002 or math 003 you may not take this course If you do sign up for this course you will not receive credit for it You should arrange as soon as possible to drop this course and sign up for the appropriate noncredit math course
Rules of the College Classroom
Professor decides where students sitA
Professor has full control over when exams are givenB
Many classes will start with QuizzesC
If you come late you will not receive any of this creditD
You are responsible for making up any material that you missedE
Class materials may not be available on days after they are given outF
No profanity G
I Classroom
II Expulsion (for the day) 3 Expulsions (not absenses) are an F
Being removed 3 times from class or vandalizing any classroom will result in an F as your class grade (Failing the entire course) Expulsion means being thrown out of class for behavior (not being absent) Vandalism will also get an F
O
H$I
Touching other people or their stuffL
Cell phone ringing Cell Phones should be in silent mode during class M
Talking on a cell phoneN
Late Assignments will not be acceptedP
Unless a doctorrsquos note or police report is submittedQ
All take home assignments must be typed R
If you are not in school when the assignment is due mail the assignmentS
Use a post office to mail the assignment toDavid SherMath DepartmentNassau Community College1 Education DrGarden City NY 11530
T 24 hour post office in NYC is located at 421 Eighth Avenue between 31st Street and 33rd Streetin the New York City borough of Manhattan across the street from Pennsylvania Station and Madison Square Garden
Hicksville Post Office Lobby Hours Mo-Fr 730am-1130pm Sa
8am-3pm 185 West John St Hicksville (OysBy)
Assignments will be returned only to the student who did them (You can not pick up your friendrsquos assignment)
U
III Assignments
IV Exams amp Withdrawel
Monday September 03 20121029 PM
mat101nc Page 1
Use a post office to mail the assignment toDavid SherMath DepartmentNassau Community College1 Education DrGarden City NY 11530
T 24 hour post office in NYC is located at 421 Eighth Avenue between 31st Street and 33rd Streetin the New York City borough of Manhattan across the street from Pennsylvania Station and Madison Square Garden
Hicksville Post Office Lobby Hours Mo-Fr 730am-1130pm Sa
8am-3pm 185 West John St Hicksville (OysBy)
Assignments will be returned only to the student who did them (You can not pick up your friendrsquos assignment)
U
Exams and quizzes are open notes open bookV
Students may not leave once they start an exam until they finishW
Cell phones and computers must be off during examsX
Students must have their college ID to take the examY
Students can withdraw till 1 week before the final They must fill out a withdrawal form or they will get a letter grade
Z
IV Exams amp Withdrawel
Use wwwtwazzupcom to search for shermat101 before class without logging in to twitter
You can also login
Text follow math4Sher To 40404
Tweets well be texted to you
off math4sher stops twitter sms
Focus on tweets containing shermat101
Using Twitter
Call 1-516-572-7383 ext 26830
State your name
Say the date and time
State which section you are in
State your phone number
Explain what you need (for example more time on an assignment)
Explain why you need it (for example you were sick and have a note from your doctor)
State times to call back
Restate your phone number
Restate your name
Restate the day and time
How to call your professor (checklist)
Email to davidbsher-fall12yahoocom
CC to DavidShernccedu
In the subject line should be your section
and what you want (briefly)
In the body State your name
explain what you need (for example more time on an assignment)
Explain why you need it (for example you were sick and have a note from your doctor)
Restate your email
Give an alternate email
If you want a phone reply give your phone
State times to call back
Grades and other course details
Grade Average Other issues
A 90 100 Getting thrown out of 3 classes for misbehavior will result in are F
Vandalizing school equipment will result in an F
Students who do not buy the textbook usually fail
Use the math center in B130 to avoid failing and to catch up
Come to the professorrsquos office hours for extra help in B3068
See the website at http wwwmatcmpnccedusherdclassdocmat101
B+ 85-90
How to email your professor (checklist)
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Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 6
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 7
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 8
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 9
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
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Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
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Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
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U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
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Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
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Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Use a post office to mail the assignment toDavid SherMath DepartmentNassau Community College1 Education DrGarden City NY 11530
T 24 hour post office in NYC is located at 421 Eighth Avenue between 31st Street and 33rd Streetin the New York City borough of Manhattan across the street from Pennsylvania Station and Madison Square Garden
Hicksville Post Office Lobby Hours Mo-Fr 730am-1130pm Sa
8am-3pm 185 West John St Hicksville (OysBy)
Assignments will be returned only to the student who did them (You can not pick up your friendrsquos assignment)
U
Exams and quizzes are open notes open bookV
Students may not leave once they start an exam until they finishW
Cell phones and computers must be off during examsX
Students must have their college ID to take the examY
Students can withdraw till 1 week before the final They must fill out a withdrawal form or they will get a letter grade
Z
IV Exams amp Withdrawel
Use wwwtwazzupcom to search for shermat101 before class without logging in to twitter
You can also login
Text follow math4Sher To 40404
Tweets well be texted to you
off math4sher stops twitter sms
Focus on tweets containing shermat101
Using Twitter
Call 1-516-572-7383 ext 26830
State your name
Say the date and time
State which section you are in
State your phone number
Explain what you need (for example more time on an assignment)
Explain why you need it (for example you were sick and have a note from your doctor)
State times to call back
Restate your phone number
Restate your name
Restate the day and time
How to call your professor (checklist)
Email to davidbsher-fall12yahoocom
CC to DavidShernccedu
In the subject line should be your section
and what you want (briefly)
In the body State your name
explain what you need (for example more time on an assignment)
Explain why you need it (for example you were sick and have a note from your doctor)
Restate your email
Give an alternate email
If you want a phone reply give your phone
State times to call back
Grades and other course details
Grade Average Other issues
A 90 100 Getting thrown out of 3 classes for misbehavior will result in are F
Vandalizing school equipment will result in an F
Students who do not buy the textbook usually fail
Use the math center in B130 to avoid failing and to catch up
Come to the professorrsquos office hours for extra help in B3068
See the website at http wwwmatcmpnccedusherdclassdocmat101
B+ 85-90
How to email your professor (checklist)
mat101nc Page 2
mat101nc Page 3
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mat101nc Page 5
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 6
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 7
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 8
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 9
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
mat101nc Page 10
mat101nc Page 11
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
mat101nc Page 13
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
mat101nc Page 26
mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
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F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
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L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
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Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
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F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
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Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
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F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
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Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
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Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
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Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
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PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
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UX
Y
U
X
Y
X is a subset of Y
X
Y
U
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U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
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Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
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`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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TWEETED REVIEWTuesday February 26 2013242 PM
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U
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Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
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Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
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IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
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30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
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A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
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L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
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Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
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5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
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quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
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Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
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o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
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at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
mat101nc Page 4
mat101nc Page 5
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 6
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 7
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 8
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 9
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
mat101nc Page 10
mat101nc Page 11
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
mat101nc Page 13
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
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mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
mat101nc Page 5
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 6
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 7
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 8
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 9
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
mat101nc Page 10
mat101nc Page 11
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
mat101nc Page 13
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
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`````````````````````````````````````
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1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
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TWEETED REVIEWTuesday February 26 2013242 PM
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U
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Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
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Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
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IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
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12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
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30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
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Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
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Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
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A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
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L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
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quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
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35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
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Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
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quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
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L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
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Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
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Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
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5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
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IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
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quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
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quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
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Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
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Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
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quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
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quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
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o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
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at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
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~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
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Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
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F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
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L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
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P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
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P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
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Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 6
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 7
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 8
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 9
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
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mat101nc Page 11
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
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Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
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PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
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UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
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mat101nc Page 19
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mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
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Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 7
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 8
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 9
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
mat101nc Page 10
mat101nc Page 11
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
mat101nc Page 13
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
mat101nc Page 26
mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
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~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Newspaper report 11 UniverseSetWhy2 universeSetWhyDue feb 14
Pg 267
Washington adams 20)45678921)R= january feb mar apr sep oct nov dec22)= sep feb apr mar jan oct dec nov Orgustjorne
Prob
dog godcod cog23)nY nh nj nm24)
Jerlie
Pg 268
129Tuesday January 29 2013307 PM
mat101nc Page 8
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 9
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
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mat101nc Page 11
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
mat101nc Page 13
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
F because 3 is not in B32)T everything in B is in A33)F 9 is not in A34)F 6 is not in C35)T36)
Pg 268
000
mat101nc Page 9
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
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mat101nc Page 11
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
mat101nc Page 13
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Set Dickey and Wakefield1Universe baseball playersWhy they throw knuckle ballsSet trailblazers of street fashion2Universe Tokyo youngstersWhy they show off their fashionsQuizA=xy2 members |A|=2a)4b)xyxyc)
131Thursday January 31 2013230 PM
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mat101nc Page 11
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
mat101nc Page 13
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
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quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
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o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
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at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
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~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
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Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
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F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
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L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
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P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
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P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
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Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
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Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
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PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
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UX
Y
U
X
Y
X is a subset of Y
X
Y
U
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U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
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Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
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`````````````````````````````````````
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1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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TWEETED REVIEWTuesday February 26 2013242 PM
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U
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Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
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Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
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IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
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12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
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30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
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Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
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A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
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L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
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35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
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Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
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L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
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Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
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Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
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5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
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Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
mat101nc Page 12
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
mat101nc Page 13
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
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mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Pg 277 prob 28
=union
M= malesS= sweatshirt
-=set difference
M-S
PCIUD
25Tuesday February 05 2013229 PM
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Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
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PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
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mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
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5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Pg 276Ex 1
2 3 4
5
6
7
8
HW pg 277 prob 25-34
U
A12
37
mat101nc Page 14
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
mat101nc Page 26
mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
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Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
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~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
PCIUDPg 277 prob 34 C=12468910D-C=3A=25689B-A=107 Pg 277 prob 33
A=25689 B=1234569 =12345689
UX
Y
27Thursday February 07 2013231 PM
mat101nc Page 15
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
UX
Y
U
X
Y
X is a subset of Y
X
Y
U
mat101nc Page 16
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
mat101nc Page 26
mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
mat101nc Page 17
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
mat101nc Page 18
mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
U
Exam 228Review 226Pg 287 ex 42
212Tuesday February 12 2013227 PM
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mat101nc Page 19
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
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Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
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mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
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A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
mat101nc Page 20
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
mat101nc Page 26
mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
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30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
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A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
mat101nc Page 21
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
mat101nc Page 22
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
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Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
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Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
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quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
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L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
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Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
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Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
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5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
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quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
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Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
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Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
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quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
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19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
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quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
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o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
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at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
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~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
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Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
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F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
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L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
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P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
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P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Report 2 Unions and Intersections2 sets same universeSets have to union or intersect in articleSet1 senior citizensSet2 kindergartenersUniverse peopleUnionWhy they were happy together
Set1 womenSet2 secretaries of stateUniverse diplomatsIntersectionWhy they did important work very wellDue 314
Reminder exam 228Review sheet image on twitter
Quiz pg 288 prob 56A= IIIB= IIIIIA =IIIIVB=IIV
214Thursday February 14 2013248 PM
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B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
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mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
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U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
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Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
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IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
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25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
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A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
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PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
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5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
B=IIV Prob 57PCIUDA=IIIB=IIIII Prob 69A=IIIIIIIVC=IIIIVVII B=IIIVVI
C=IVVIVIIIII
mat101nc Page 23
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
mat101nc Page 26
mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
mat101nc Page 24
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
`````````````````````````````````````
mat101nc Page 25
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
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mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
1)
H=VVIVIIIV2)H=IIIIIIVIIIF=IIIIVV G=IIIIIVVI
3)
226Tuesday February 26 2013247 PM
mat101nc Page 26
mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
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Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
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Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
mat101nc Page 27
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
TWEETED REVIEWTuesday February 26 2013242 PM
mat101nc Page 28
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
U
mat101nc Page 29
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Handout pg 13Paris milan tokyo
Set1 fashion trailblazersSet2 japanese peopleUniverse peopleIntersectionWhy because they are interesting to western designers
Set1 American fashion buyersSet2 European fashion buyersUniverse fashion buyersUnionWhy buying bagfuls of Japanese designs
Pg 10 handoutSet1 hip looking peopleSet2 New yorkersUniverse peopleIntersectionWhy they crowded into landmarks Sunshine Cinema
Pg 17Set1 people in United statesSet2 people in Europe
35Tuesday March 05 2013246 PM
mat101nc Page 30
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Set2 people in EuropeUniverse peopleUnionWhy they had different opinions about universal high school
Set1 dishwashersSet2 college graduatesUniverse peopleIntersectionWhy dishwashers who are college graduates make more money
Pg299 book Ex 1
U
I IIIII
IV
CS
25=|U|=I( 10 ) + II( 3 ) + III( 4 ) + IV( 8 )
mat101nc Page 31
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
IV( 8 )ANSWER III(4)
PG 301 EX 9
U
9=|A|=I( ) + II( )
7=|S| = II( ) + III( )12=
mat101nc Page 32
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
12=
60=|U|=I( 5 )+II( 10 )+III( 5 )+IV( 8 )+V( 7 ) +VI( 13 )+ VII( 2 )+VIII( 10 )30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )
mat101nc Page 33
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
30=|R|=I( 5 )+II( 10 )+IV( 8 )+V( 7 )30=|P|=IV( 8 )+V( 7 )+VI( 13 )+VII( 2 )35=|G|=II( 10 )+III( 5 ) +V( 7 )+VI( 13 )
I(5)A)VIII(10)B)
HWPG 301-302 problems 8-12
mat101nc Page 34
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Exam 2 on 42Review on 321
Universe football playersSet1 quaterbacksSet2 runningbacksIntersectionWhy Tim Tebow is both
Universe PeopleSet1 Yankees playersSet2 injured peopleIntersectionWhy many Yankees are injured
Universe SoldiersSet1 North korean soldiersSet2 UN soldiersUnionWhy they may start fighting again
Universe CollegesSet1 community collegesSet2 4 year collegesUnionWhy they plan to work together to increase graduation
100=|U|=I( 34 )+II( 9 )+III( 6 )+ IV( 5 )+V(2 )+VI( 8 ) + VII( 25 )+VIII( 11 )50=|M|=I( 34 )+II( 9 )+IV(5 )+V( 2 )25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
37Thursday March 07 2013246 PM
mat101nc Page 35
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
25=|S|=II( 9 )+III( 6 )+V( 2 )+VI( 8 )40=|E|=IV( 5 )+V( 2 )+VI( 8 )+VII(25 )
VIII(11)B)HW READ 55
A) III(6)
mat101nc Page 36
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
mat101nc Page 37
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
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w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Pg 302 prob 12Exam 42
75=|U|=I( 5 ) + II(26 )+III( 0 )+IV( 28 )+V(2 )+ VI( 1 )+VII(13 )+VIII( 0 )29=|S|=II(26 )+III( 0 )+V( 2 )+VI( 1 )44=|C|=IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )
I(5)a)|S|=I(5)+IV(28)+VII(13)+VIII(0) =46b)I(5)+III(0)+VII(13)=18c)PG 302 prob 11
312Tuesday March 12 2013231 PM
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19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
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30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
19=|G|=I( )+II( )+IV( )+V( )19=|S|=II( )+III( )+V( )+VI( )20=|B|=IV( )+V( )+VI( )+VII( )
IIIIVVVII-IIIIIVVII(2)IV(2)VII(2)=6
HW READ 55 pg309 ex 1
mat101nc Page 38
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
A=IIIIVVB=IIIIIVVI C=IVVVIVII C-A=VIVIIC-B=IVVII
314Thursday March 14 2013236 PM
mat101nc Page 39
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
PG 307Simplifiers 1678910Rearrangers 234511
(X-Y) GIVEN
X-Y L1
X-X GIVEN
L11 A IS X B IS X
L8 A IS X
GIVEN
L2 A IS X B IS
L3 A IS Y B IS X C IS X
L8 A IS X
mat101nc Page 40
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
L10 A IS Y
GIVEN
( L4 A IS X B IS Y C IS X
( L8 A IS X
L10 A IS
HW pg 310-311Prob 20-22
mat101nc Page 41
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
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EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
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Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
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F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
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ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
quiz pg 310 prob 20
L11 A is P B is Ra)L5 A IS P B IS R L1 A IS Rb)L3 A IS P B IS R C IS Rc)L8 A IS Rd)L10 A IS Pe)
PG 311 PROB 21L5 A IS P B IS S L1 A IS SA)L4 A IS S B IS P C IS SB)L8 A IS SC)L10 A IS D)L11 A IS S B IS PE)
PG 309 EX1L11 A IS A B IS A)L5 A IS B B IS A L1 A IS BB)L4 A IS A B IS B C AC)L8 A IS AD)L10 A IS E)
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
a-b=a
319Tuesday March 19 2013230 PM
mat101nc Page 42
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
30 pts
1 Use the regions of this Venn Diagram to show
XYXYYXY
U
XY
I II III
IV
35 pts
U
IIIIIIIV
3 30 insects were found in the jungle 10 of the bugs have purple wings 18 of the bugs have green heads 22 of the bugs have purple wings or green heads What is the number of30=|U|=I( 4 )+II( 6 )+III( 12 )+IV( 8 )10=|P|=I( 4 )+II( 6 )18=|G|=II( 6 )+III( 12 )22=
Bugs with green headsa)
18
Bugs with a green head and not purple wingsb)
III(12)
Bugs with purple wings or not green headsc)
35 pts
X=IIIY=IIIIIX=IIIIV Y-X=III(Y-X)=IIIIV
Review Exam 321Thursday March 21 2013249 PM
mat101nc Page 43
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
35 pts
4 Fill in the laws and assignments in this proof
Statement Law Assignment
GIVEN
L11 A is M B IS R
L11 A IS
L5 A IS M B IS R
L1 A IS R
L2
A IS M B IS
L6 A IS M B IS R
L6 A IS A B IS BAL11 A IS B B IS A L1 A IS ABL4 A IS A B IS B C IS ACL7 A IS ADL2 A IS A B IS EL6 A IS A B IS BF
PG 309 EX 2
mat101nc Page 44
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Pg 311
L10 A is Ca)L10 A IS Ab)L11 A IS B IS A L1 A IS Ac)L5 A IS C B IS Ad)L2 A IS C B IS e)L4 A IS C B IS C C IS Af)L8 A IS Cg)L10 A IS h)L11 A IS C B IS Ai)
EX 23 L8 A IS B L10 A IS AEX 25 L4 A IS A B IS A C IS C L8 A IS A L10 A IS
EX 31
Ex 22
44Thursday April 04 2013247 PM
mat101nc Page 45
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
EX 31 L11 A IS P B IS R L5 A IS P B IS R L1 A IS R L4 A IS P B IS P C IS R L8 A IS P L10 A IS
HW PG 311 EX 24-32READ 63
mat101nc Page 46
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
quiz pg 311 ex 30
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
Statement Law Assignment
GIVEN
L8 A IS R
L9
L11 A IS R B IS S
L10 A IS
L3 A IS R B IS S C IS S
L8 A IS S
L10 A IS R
SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS X B IS Y
L5 A IS X B IS Y
L1 A IS Y
L2 A IS X B IS Y
PG 311 EX 31 SHOW
STATEMENT LAW ASSIGNMENT
GIVEN
L11 A IS P B IS R
49Tuesday April 09 2013227 PM
mat101nc Page 47
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
L11 A IS P B IS R
L5 A IS P B IS R
L1 A IS R
( L4 A IS P B IS P C IS R
L8 A IS P
L10 A IS
There are 20 students in a class 13 of them are women what is the proportion of women1320
Universe studentsSet womenProportion 1320Why women are a bit more likely to take the class than men
90 of people surveyed say background checks should be performed on gun sales
Universe people surveyedSet people who say background checks should be performedProportion 90Why to show how popular background checks are
90=
63 of 100 senators voted for the billProportion is 63100Universe senators who voted
mat101nc Page 48
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Universe senators who votedSet senators who voted for the billWhy to show how close the vote was
Report 3 due 425
mat101nc Page 49
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Most of the students in the class will passUniverse studentsSet passing studentsProportion mostWhy to reassure class
The yankees have won 4 games and lost 3
Universe Yankee gamesSet Games wonProportion 47Why to show they are doing better than expected
Rangers won 20 lost 15 tied 3Universe ranger gamesSet games wonProportion 2038
60 of american teenagers are overweight or obeseUniverse american teenagersSet overweight or obese teenagersProportion 60 or 60100Why to explain why schools are eliminating sugary drinks
In a doctors office there are 25 patients10 have fevers15 have coughs5 have both
411Thursday April 11 2013235 PM
mat101nc Page 50
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
5 have both
What is the proportion of patients with fevers1025
What is the proportion of patients with neither
25=|U|=I( 5 )+II( 5 )+III( 10 )+IV( 5 )10=|F|=I( 5 )+II( 5 )15=|C|= II( 5 )+III( 10 )
NEITHER= IV(5)|U| = 525 = 02
PROPORTION OF PEOPLE WITH COUGHS OR FEVER
PROPORTION OF FEVER PATIENTS WITH COUGHS
PROPORTION OF COUGH PATIENTS WITH FEVER mat101nc Page 51
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
PROPORTION OF COUGH PATIENTS WITH FEVER
INDEPENDENCE COUGHS ARE INDEPENDENT OF FEVERS IFTHE PROPORTION OF COUGH PATIENTSIS THE SAME AS THE PROPORTION OF FEVER PATIENTS WITH COUGHS
NOT INDEPENDENT
At a restaurant there were 100 diners 70 of them had salad 60 of them had chicken 40 had both 30 of the diners who had chicken got sick 40 of the diners who had salad got sick 60 diners got sick 20 had both and got sick
I
II
III
IV
VVI
VIII
SALAD
CHICKEN
mat101nc Page 52
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
IVVII
SICK
100 = |U|=I( 10 )+II( 20 )+III( 10 )+IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )+VIII( 0 )70=|SALAD|=I( 10 )+II( 20 )+IV( 20 )+V( 20 )60=|CHICKEN|=II( 20 )+III( 10 )+V( 20 )+VI( 10 )60=|SICK|=IV( 20 )+V( 20 )+VI( 10 )+VII( 10 )40=|CHICKEN AND SALAD|=II( 20 )+V( 20 )30=|CHICKEN AND SICK| = V( 20 )+VI( 10 )40=|SALAD AND SICK| = IV( 20 )+V( 20 )
Is sick independent of chicken P(SICK)= 60100=06
P(SICK|CHICKeN)=
Chicken made sick less likelyIs sick independent of salad
P(SICK|SALAD)=
HW read chapter 1
mat101nc Page 53
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
quiz 12 pizza 4 have onions 3 have garlic 6 have neither onion or garlic Is onion independent of garlic show work
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
U
Handout pg 16Bottom of first collumnUniverse Scanned stuffSet photographsProportion 500000(170000+250000+610000+200000+500000)why to show what kind of stuff Norway is scanning
Bottom of pageIt was engineered so that 99999 of the time you could make a phone callUniverse timeSet times when we can make a phone callProportion 99999Why to show how reliable phones are
Pg 13Graph 50 bondUniverse $100000
O
G
12=I( 3 )+II( 1 )+III( 2 )+IV( 6 )4=I( 3 )+II( 1 )3=II( 1 )+III( 2 )
P(O)=P(O|G)P(O)= 412 = 03333
13=03333 They are independent
416Tuesday April 16 2013228 PM
mat101nc Page 54
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Universe $100000Set bond part of the investmentProportion 50Why to show how a mix of investments performs
Batting average is hits at bats
mat101nc Page 55
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
quiz 24 animals 16 eat meat 18 eat vegetables 4 eat only vegetables Is meat eating independent of vegetable eating
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=typdgt
24=I( 2 )+II( 14 )+III( 4 )+IV( 4 )16=I( 2 )+II( 14 )18=II( 14 )+III( 4 )
dependent
Logic
418Thursday April 18 2013240 PM
mat101nc Page 56
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Logic Verbs
m=The man ate the cat
Statements with verbs can be true or false
mTF
a = The man was arrested
m a
T T
F T
T F
F F
P N A O C B() ~
Not - negation ~
m ~m mat101nc Page 57
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
m ~m
T F
F T
And - conjunction
m a ~m
T T T F F F
F T F T T T
T F F F F T
F F F T F T
or - disjunction
m a ~m
T T T F T F
F T T T T F
T F T F F F
F F F T T T
implies - conditional
m a ~m
T T T F T F mat101nc Page 58
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
T T T F T F
F T T T T F
T F F F T T
F F T T f F
Is equivalent - biconditional
m a ~m
T T T F F F
F T F T T T
T F F F T T
F F T T F F
HWpg 8 prob 22-37
Pg 15 has a general table
mat101nc Page 59
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Pg 8
Tf statement b22Tf statement c23Disjunction 24Biconditional 25Conjunction 26Conditional 27Conditional conjunction 28Conjuction 29Conditional 30
Quiz Ex 22242628
P N A O C B() ~
a b c
T T T
F T T
T F T
F f T
T T F
F T F
T F F
F f f
422Tuesday April 23 2013239 PM
mat101nc Page 60
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
F f f
a b
T T T T T
F T T F T
T F F T T
F F T T T
Contradiction is all F
Pg 29Ex 2
p q
T T T T
F T F T
T F F F
F F F T
HWPg 30 prob 11-18Pg 38 prob 11-14
mat101nc Page 61
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
quiz pg 30 prob 16
Pasted from lthttpstwittercomsearchrealtimeq=23shermat101ampsrc=typdgt
Report 4 due 592 statements Every statement needs a verb
spiderman saved Mary Jane but he got no credit for doing itStatement 1 spiderman saved mary janeStatement 2 he gets no credit for doing itConjunctionWhy to give spoilers for the plot of the movie
Statements need to be near each other Conjuction words and but also
Disjunction almost always an orDisjuctions are about choice
Conditionals usually if
if you go abroad you must remember your passportStatement 1 you go abroadStatement 2 you must remember your passportConditionalWhy reminders for avoiding travel issues
Pg 30 prob 16PNAOCB
p q p -gt q ~p ~p v q (p -gt q) -gt (~p v q)
T T T F T T
F T T T T T
T F F F F T
F F T T T T
Tautology
19
425Thursday April 25 2013240 PM
mat101nc Page 62
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
19
p ~p q ~q ~p v ~q
T F T F F F T
F T T F T T T
T F F T T F T
F T F T T F T
Tautology
Pg 38 Prob 13
q r p ( [ (
T T T T T T T T T
F T F T F F T F T
T F F T f T F F T
F F F T f f F F T
T T T F T T T T T
F T F F T T T T T
T F F F T T T T T
F F F F t T T T T
HW read 21
mat101nc Page 63
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
quiz pg 38 prob 12
Pasted from lthttpstwittercomsearchq=23shermat101ampsrc=savsgt
PNAOCB
Pg 18Steve Dickey also said his grand parents would tell him that the great yankee catcher bill dickey was a distant cousing of his great grandfather But even with that baseball linear he chose dentistry
ConjunctionStatement 1 Steve Dickey also said his grand parents would tell hellipStatement 2 even with that baseball lineage he chose dentistry Why to explain the connection between the dickeys and baseball and dentistry
Pg 16DisjunctionStatement 1 Many American institutions have concentrated on making scans of their own special treasuresStatement 2 American institutions are collaborating with one another on themed projectsWhy to discuss the variety of approaches to scanning in America
Pg 14If I could I would stay here long termConditional
430Tuesday April 30 2013231 PM
mat101nc Page 64
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
ConditionalStatement 1 I couldStatement 2 I would stay here long termWhy to show the opinion of an immigrant to japan
ConjunctionStatement 1 if I could I would stay here long termStatement 2 it is not so easyWhy to show the opinion of an immigrant to japan
p ~p q ~p v q ~q r ~q v r
T F T T F T T T
F T T T F T T T
T F F F T T T T
F T F T T T T t
T F T T F F F T
F T T T F F F T
T F F F T F T T
F T F T T F T t
If I get an a then I will be happyEither my average is over 90 or I wont get an aMy average is over 90 Therfore I will be happy
a -gt ho v ~ao
mat101nc Page 65
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
o v ~ao-----------h
o a ~a o v ~a h a -gt h
T T F T T T
F
T F T T T T
T T F T F F
T F T T F T
HWPg 84-85Pr0blems11-16
mat101nc Page 66
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
at that point in my life I could continue with the same old stuff or take on a big new challenge
DisjunctionStatement 1 at that point in my life I could continue hellipStatement 2 take on a big new challengeWhy to show how he became an important leader
Pg 14 last columnif we knewhellip
ConditionalStatement 1 we knew that beating up on you hellipStatement 2 we would have done it tooWhy to show maffeis attitude towards promoting
p ~p q q -gt p c
T F
F T T F T F
F T F T T T
F T T F F F
F T F T F F
Pg 85 ex 19~a~m v a~m -gt p----------
52Thursday May 02 2013254 PM
mat101nc Page 67
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
~m v a~m -gt p----------p v a
a ~a m ~m ~m v a p ~m -gt p p v a
T F
F T T F F
F T F T T T T T
F T F T T F F
Prob 21
r s g s -gt g r v (s -gt g)
T T T T T
F
T F T T T
T T F F T
T F F T T
mat101nc Page 68
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Quiz pg 85 ex 24Exam 514 review 59 class cancelled 516 unless emergency on 514
r q q-gtr p p-gtq
T T T T T
F
T F T T F
T T T F T
T F T F T
Pg 85 ex 23
p q p-gtq S ~s ~s v q
T T T T F T
F
T F F
T T T F T T
Pg 95 ex 55
s = I take the subway to workm = I spend moneye = I get exercisew = I walk to work
57Tuesday May 07 2013235 PM
mat101nc Page 69
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
w = I walk to work
m ~m w s s-gtm ~s e ~s-gte
T F T F
F T T T T F
T F F F
F T F F
F T T T F T T T T
F T T T F T T F F
Pg 95 ex 57h = the dish is hots = the dish is spicyo = nick will order it
h ~h s o
T F
F T T F T T T
F T F F T T T
F T T F T F F
F T F F T F F
mat101nc Page 70
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
F T T F T F F
F T F F T F F
HwPg 95Prob 56 58
mat101nc Page 71
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
Review 101 Exam 3 AMay 13Show your work on each problem25 pts1 Validate the argument below with truth table
m ~m g z g-gtz (g-gtz) v m
T F T F
F T T T T T T
T F F F
F T F F
F T T T F F F
25 pts2 Show
with a statement reason proof
GIVEN
L11 A IS Y B IS X
L5 A IS Y B IS X
L1 A IS X
L3 A IS Y B IS Y C IS X
L8 A IS Y
Review exam 3Thursday May 09 2013244 PM
mat101nc Page 72
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
L8 A IS Y
L10 A IS X
Y-X L10 A IS Y-X
L11 A IS Y B IS X
25 pts
3 Write the equivalent symbolic logic for the argument below
I bring my notes to the exam or I remember everything If I remember everything then I would have gotten Arsquos in math before I did not get Arsquos in math Therefore I bring my notes to class
n = I bring my notes to the examr = I remember everythinga = I get As
25 pts
a) Is drinking beer independent of drinking scotch
b) Is drinking beer independent of drinking rye
c) Is drinking rye independent of drinking scotch
4 There are 90 men at a bar 70 are having beer 27 are having scotch (some may be having beer too) 9 drank some rye 1 had rye but no beer and no scotch 1 had rye and scotch and no beer 6 had scotch but no beer 3 are having all three drinks
mat101nc Page 73
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
P(X)=|X||U|P(X|Y) = |X Y||Y|
90 = I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI( 1 )+VII( 1 )+VIII( 13 )70=I( 45 )+II( 18 )+IV( 4 )+V( 3 )27=II( 18 )+III( 5 )+V( 3 )+VI( 1 )9=IV( 4 )+V( 3 )+VI(1 )+VII( 1 )6=III( 5 )+VI( 1 )
1 P(B)= 7090=07778
P(B|S)=
= (18+3)27=07778 YES INDEPENDENT
2 P(B|R)=
= (4+3)9=07778 YES INDEPENDENT
3 P(R)= 990=01
p(R|S)=
(3+1)27=01481 NO DEPENDENT
B S
R
mat101nc Page 74
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75
P(X)=|X||U|P(X|Y) = |X Y||Y|IF THE SAME X INDEPENDENT OF Y
mat101nc Page 75