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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<ul><li><p>MAT225:DiscreteMathematics ReviewSheetfor FinalExam (Ensley)</p><p>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: </p><p> Determinethe nthtermofasequence. Findarecursiveformulaforasequence. Findaclosedformulaforasequence.</p><p>Section1.3 Fillin truthtablesinvolvingnegation,and,andorstatements. Usingtruthtablesdeterminewhetherornottwopropositionsarelogicallyequivalent. Given anEnglishsentence,rewriteitusingpropositionallogicandviceversa. Negateandstatementsandorstatements.</p><p>Section1.4 Determinewhetherpropositionsarisingfrompredicatesaretrueorfalse. Recognizequantifiers(forallandthereexists.) Constructcounterexamplesforfalsestatements. Negatepredicatestatements. WriteEnglishsentencesusingquantifiersandpredicates,andviseversa.</p><p>Section1.5 BeabletowriteEnglishifthenstatementsusingpropositionallogicandpredicates. Fillin truthtablesinvolvinganimplicationsstatementandunderstandwhenanifthenstatementisfalse. Negate implicationstatementsaswellasimplicationstatementsinvolvingquantifiers. Writetheconverse,inverse,andcontrapositiveofanimplicationstatement. Determineififthenstatementsaretrueorfalse,andiffalse,beabletofindacounterexample.</p><p>Section2.1 Knowthedefinitionofevenandoddintegers. Beableto do followyournosetypesofproofsinvolvingfactsaboutevenandoddintegers. Readastatementanddetermineifitistrueorfalse,andifitisfalse,findacounterexample. Write(andprove)thecontrapositiveofanimplicationstatement</p><p>Section2.2 Knowthedefinitionofdivisibility. Proveresultsaboutdivisibilityandrationalnumbers. Knowhowtostateandinterpretthedivisiontheorem. Computemod.</p><p>Section2.3 Doboth typesofinductionproofs(sequencesand sums).</p><p>Section2.6 Convertbase10numberstootherbasesandviceversa.</p><p>Section3.1 Understandsetnotation,thatis,besurethatgivenaset,youcanwritedowntheelementsthatbelongtothat</p><p>set. Findthe union,intersection,setdifference,andcomplementofsets. Understandthedifferencebetweenbeinganelementofasetandbeingasubsetofaset. Writesetsusing aformdescription. Writesetsusing apropertydescription. ShadeVenndiagramsappropriately. Beabletocompute n(A)foragivensetA. Knowtheinclusionexclusionprinciplefortwosets.</p><p>Section3.2 BeabletocomputetheCartesianproductoftwosets. Beabletofindthepowersetofagivenset.</p></li><li><p> Knowthedefinitionofapartition.Section3.3 </p><p> ProvesetidentitiesbyquotingappropriatepropertiesofsetsSection3.4 </p><p> ProveBooleanalgebraidentitiesbyquotingappropriatepropertiesofBooleanalgebrasystems. KnowtheconnectionbetweenBooleanalgebranotationandsetnotation</p><p>Section3.5 ConstructalogiccircuitgivenaBooleanalgebra WriteaBooleanlogicexpressionwhichcorrespondstoagivenlogiccircuit UseaKarnaughmaptosimplifyasumofproductsBooleanalgebraexpression</p><p>Section4.1 Knowthedefinitionoffunction,relation,inversefunction,andinverserelation. Beabletodrawanarrowdiagramtorepresentafunctionand/orrelation. Givenarelation/functionbeabletofinditsinverse(viaanarrowdiagram),ifitexists.</p><p>Section4.2 Determinethecomposition oftwofunctionsusingtables,arrowdiagrams,andalgebra. Determinethecompositionoftworelationsusinganarrowdiagram. InterpretthecompositionoftworelationsusinganEnglishsentence.</p><p>Section4.6 Usepropertieslogarithmstodeterminethenumberofdigitsofaninteger. Knowhowtodocomputationsinvolvingfloorandceilingfunctions</p><p>Section5.1 Identifywhetheracountingproblem shouldberepresentedasset,permutation,orderedlist,orunorderedlist Explain(withoutcounting)whytwoseeminglydifferentcountingproblemshavethesamenumericanswer</p><p>Section5.2 Applytheproductruleforcounting Applythesumruleforcounting.</p><p>Section5.3 Recognizeacombination(set)problemandbeabletosolveit</p><p>Section5.4 Countbinarysequencesandotherorderedliststypesofproblems Recognizeandcountunorderedlistsproblems(suchasbagproblems)</p><p>Section6.1 Determinethesamplesizeofanexperiment Findtheprobabilityofequallylikelyevents UsethefactthatP(E)+P(E)=1</p><p>Section7.1 Knowdefinitionsassociatedwithagraph(e.g.,walk,trail,circuit,cycle,degree,Euleriancircuit,Eulerian</p><p>path,connected) DeterminewhetherornotagraphcontainsanEuleriancircuitorEulerianpath. Find thedegreesequenceofagraphandproducegraphwithagivendegreesequence,ifpossible.</p><p>Section7.2 Determinewhetherornottwographsareisomorphic.</p><p>Section7.4 Findanadjacencymatrixforagivengraph. ComputeandinterpretMkandM1+M2++Mk. Understandtheconnectionsbetweenbinaryrelations,directedgraphs,andadjacencymatrices. Understandtheconnectionsbetweenrelationcompositionand Booleanmatrixarithmetic.</p></li></ul>

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