set theory and venn diagrams t bolan. words used to describe automobiles cars motorcycles trucks...
TRANSCRIPT
SET THEORY and
VENN DIAGRAMS
T Bolan
Words used to describe Automobiles
Cars
Motorcycles
Trucks
4-wheelers
2-wheelers
18-wheelers
3-wheelers
Ford
Mitsubishi Farrari
2-door
4-door
vans Old
new
gas
diesel Solar
green red
blue
We can use these words to categorize cars into types
Cars
Motorcycles
Trucks
4-wheelers
2-wheelers
18-wheelers
3-wheelers
Ford
Mitsubishi Farrari
2-door
4-door
vans Old
new
gas
diesel Solar
green red
blue
Now, pretend for a second that this box, represents “Crazy Bob’s Autos” parking lot.
And everyone sold their car to Crazy Bob
So he has every car in existence,
Every car in existence
motorcycles 18-wheelers
Blue cars
1. Where do I go to find a motorcycle?
Where do I Find an 18-wheeler?
3. Where do I get aBlue car?
Where would I lookto find a blue car if I don’t want an 18-wheeler?
Where would I lookto find a blue car if I don’t want an 18-wheeler or a motorcycle?
What about if I wanta motorcycle but not a blue one?
What If I don’t care what I buy, as longas it isn’t blue?
These are pretty easy
it actually takes longer to read the questionthan it does to answerit.
Let’s simplify this
The symbol means INTERSECTION
It means both.
If you want a blue motorcycle,
Then you want blue and motorcycle
MB
The symbol means UNION
It means either.
If you want any Motorcycle ORAnything Blue
MB
What does this look like?
EB
What does this look like?
EB
What does this look like?
EM
What does this look like?
EM They don’t overlap.
There is no such thing
Here we are asked for a Motorcycle that is also an 18-wheeler
When there is no answer,We call it the EMPTY SET
Or NULL SET
Before we go any further, let’s make sure we understand the NULL SET.
It is not the same as zero.
How many donkeys have walked on the moon?
0
How many donkeys should you eat to turn your hair purple?
Zero donkeys is not the right answer.
This question has no answer. Something is wrong with the question.
NULL SET
If we draw a bar above it. It means the opposite.
EM
EM
“I want a motorcycle or an 18-wheeler”
“Anything but motorcycle or an 18-wheeler”
E
E
“I want an 18-wheeler”
“Anything but an 18-wheeler”
BM
BM
“I want a blue motorcycle”
“Anything but a blue motorcycle”
B“I don’t care what I get, as long as it isn’t blue”
In the box is every student in the school.
M for kids in your MATH class
S for kids in your SCIENCE class
G for kids in your GYM class
Students in Math OR Science Students in Math AND Science
Students in Math AND Science AND Gym
Students NOT in Gym or Math
SM SM
GSM GM
Students NOT in Gym or Math Students NOT in Gym AND Math
GM
In other words: you start to tell a joke in math class, but the bell ringsAnd you have to finish it in gym.
Who DOESN’T get the joke?These guys heard the whole joke
Sooo everyone else
GM
SM SM SM
SM SMSM
