# MAT 225: Discrete Mathematics Review Sheet for Final 225: Discrete Mathematics Review Sheet for Final Exam (Ensley) The f ... • Construct a logic circuit given a Boolean algebra

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• MAT225:DiscreteMathematics ReviewSheetfor FinalExam (Ensley)

Thefinal examwillcoversections1.21.5,2.12.3,2.6,3.13.5,4.14.2,4.6,5.15.4,5.6,6.1,7.1,7.37.4. Youareresponsibleforallclassnotes,homeworkexercises,andquizandexam problems. Tobesuccessfulontheexam,youshouldbeableto do thefollowing:Section1.2:

Determinethe nthtermofasequence. Findarecursiveformulaforasequence. Findaclosedformulaforasequence.

Section1.3 Fillin truthtablesinvolvingnegation,and,andorstatements. Usingtruthtablesdeterminewhetherornottwopropositionsarelogicallyequivalent. Given anEnglishsentence,rewriteitusingpropositionallogicandviceversa. Negateandstatementsandorstatements.

Section1.4 Determinewhetherpropositionsarisingfrompredicatesaretrueorfalse. Recognizequantifiers(forallandthereexists.) Constructcounterexamplesforfalsestatements. Negatepredicatestatements. WriteEnglishsentencesusingquantifiersandpredicates,andviseversa.

Section1.5 BeabletowriteEnglishifthenstatementsusingpropositionallogicandpredicates. Fillin truthtablesinvolvinganimplicationsstatementandunderstandwhenanifthenstatementisfalse. Negate implicationstatementsaswellasimplicationstatementsinvolvingquantifiers. Writetheconverse,inverse,andcontrapositiveofanimplicationstatement. Determineififthenstatementsaretrueorfalse,andiffalse,beabletofindacounterexample.

Section2.3 Doboth typesofinductionproofs(sequencesand sums).

Section2.6 Convertbase10numberstootherbasesandviceversa.

Section3.1 Understandsetnotation,thatis,besurethatgivenaset,youcanwritedowntheelementsthatbelongtothat

set. Findthe union,intersection,setdifference,andcomplementofsets. Understandthedifferencebetweenbeinganelementofasetandbeingasubsetofaset. Writesetsusing aformdescription. Writesetsusing apropertydescription. ShadeVenndiagramsappropriately. Beabletocompute n(A)foragivensetA. Knowtheinclusionexclusionprinciplefortwosets.

Section3.2 BeabletocomputetheCartesianproductoftwosets. Beabletofindthepowersetofagivenset.

• Knowthedefinitionofapartition.Section3.3

ProvesetidentitiesbyquotingappropriatepropertiesofsetsSection3.4

ProveBooleanalgebraidentitiesbyquotingappropriatepropertiesofBooleanalgebrasystems. KnowtheconnectionbetweenBooleanalgebranotationandsetnotation

Section3.5 ConstructalogiccircuitgivenaBooleanalgebra WriteaBooleanlogicexpressionwhichcorrespondstoagivenlogiccircuit UseaKarnaughmaptosimplifyasumofproductsBooleanalgebraexpression

Section4.1 Knowthedefinitionoffunction,relation,inversefunction,andinverserelation. Beabletodrawanarrowdiagramtorepresentafunctionand/orrelation. Givenarelation/functionbeabletofinditsinverse(viaanarrowdiagram),ifitexists.

Section4.2 Determinethecomposition oftwofunctionsusingtables,arrowdiagrams,andalgebra. Determinethecompositionoftworelationsusinganarrowdiagram. InterpretthecompositionoftworelationsusinganEnglishsentence.

Section4.6 Usepropertieslogarithmstodeterminethenumberofdigitsofaninteger. Knowhowtodocomputationsinvolvingfloorandceilingfunctions

Section5.2 Applytheproductruleforcounting Applythesumruleforcounting.

Section5.3 Recognizeacombination(set)problemandbeabletosolveit

Section5.4 Countbinarysequencesandotherorderedliststypesofproblems Recognizeandcountunorderedlistsproblems(suchasbagproblems)

Section6.1 Determinethesamplesizeofanexperiment Findtheprobabilityofequallylikelyevents UsethefactthatP(E)+P(E)=1

Section7.1 Knowdefinitionsassociatedwithagraph(e.g.,walk,trail,circuit,cycle,degree,Euleriancircuit,Eulerian

path,connected) DeterminewhetherornotagraphcontainsanEuleriancircuitorEulerianpath. Find thedegreesequenceofagraphandproducegraphwithagivendegreesequence,ifpossible.

Section7.2 Determinewhetherornottwographsareisomorphic.