本文格式為Word版，下載可任意編輯——離散數(shù)學(xué)英文版答案DiscreteMathematicTestEditor:JinPengDate:2022.5.6Contents:DiscreteMathematicTest(Unit1)3DiscreteMathematicTest(Unit2)8DiscreteMathematicTest(Unit3)13DiscreteMathematicTest117DiscreteMathematicTest222Appendix1AnswertoDiscreteMathematicTest(Unit1)27Appendix2AnswertoDiscreteMathematicTest231DiscreteMathematicTest(Unit1)PartI(T/Fquestions,15Scores)Inthispart,youwillhave15statements.Makeyourownjudgment,andthenputT(True)orF(False)aftereachstatement.1.LetA,B,andCbesetssuchthatA∪B=A∪C,thenB=C.()2.LetAandBbesubsetsofasetU,andAíB,thenA△B=A-BandA∩B’=?.()3.Letpandqandrbethreestatements.If~pú~q≡~pú~r,thenqandrhavethesamevalue.()4.LetA,BbesetssuchthatbothAíBandA?Bispossible.()5.Letpandqbetwostatements,then(p?～q)?(（～pú～q）?(p?～q))isatautology.()6.LetA,Bbesets,P(A)isthepowersetofA,thenP(A-B)=P(A)-P(B).()7.LetA,B,andCbesets,thenifA?B，BíC，thenAíC.()8.LetA,Bbesets,ifA={?},B=P(P(A)),then{?}?Band{?}íB.()9.Letxberealnumber,thenx?{x}-{{x}}and{x}í{x}-{{x}}.()10.LetA,B,andCbesets,thenA-(B∪C)=(A-B)∪(A-C).()11.IfA={x}∪x,thenx?AandxíA.()12.(“x)（P(x)∧Q(x)）and(“x)P(x)∧(“x)Q(x)areequivalent.()13.LetAandBbesets,thenA×(B-C)=(A×B)-(A×C).()14.Theargumentformula(púq)?(rùs),(sút)?w╞p?wisvalid.()15.(“x)（P(x)?Q(x)）and(“x)P(x)?(“x)Q(x)areequivalent.()PartII(1Foundations:SetsLogic,andAlgorithms,85Scores)1.(8points)WhatsetssoeachoftheVenndiagramsinfollowingFigurerepresent?2.(8points)LetU={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}.LetA={1,5,6,9,10,15}andB={5,6,8,9,12,13}.Determinethefollowing:Finda.SAb.SA’c.SBd.SA∩B.3.(8points)Aclassof45studentshas3minorsforoptions,respectivelyA,BandC.Aisthesetofstudentstakingalgebra,Bisthesetofstudentswhoplaybasketball,Cisthesetofstudentstakingthecomputerprogrammingcourse.Amongthe45students,12choosesubjectA,8chooseBandanother6chooseC.Additionally,9studentschooseallofthethreesubjects.Whatistheatleastnumberofstudentsdonottakingthealgebracourseandthecomputerprogrammingcourseandplayingbasketball?4.(8points)FindaformulaAthatusesthevariablespandqsuchthatAistrueonlywhenexactlyoneofpandqistrue.5.(8points)Provethevalidityofthelogicalconsequences.AnneplaysgolforAnneplaysbasketball.Therefore,Anneplaysgolf.6.(9points)Provethevalidityofthelogicalconsequences.Ifthebudgetisnotcutthenpricesremainstableifandonlyiftaxeswillberaised.Ifthebudgetisnotcut,thentaxeswillberaised.Ifpriceremainstable,thentaxeswillnotberaised.Therefore,taxeswillnotberaised.7.(8points)(1)Whatistheuniversalquantificationofthesentence:x2+xisaneveninteger,wherexisaneveninteger?Istheuniversalquantificationatruestatement?(2)Whatistheexistentialquantificationofthesentence:xisaprimeinteger,wherexisanoddinteger?Istheexistentialquantificationatruestatement?8.(12points)Symbolizethefollowingsentencesbyusingpredicates,quantifiers,andlogicalconnectives.(1)Anynaturenumberhasonlyonesuccessornumber.(2)Forallx,y?N,x+y=xifandonlyify=0.(3)Notallnaturenumberx?N,itexistanaturenumbery?N,suchthatx≤y.9.(8points)Showthat“x（～F(x)∨A(x)），“x（A(x)→B(x)），$xF(x)|=$xB(x)10.(8points)Inthebubblesortalgorithm,ifsuccessiveelementsL[j]andL[j+1]aresuchthatL[j]>L[j+1],thentheyareinterchanged,thatis,swapped.Therefore,thebubblesortalgorithmmayrequireelementstobeswapped.Showhowbubblesortsortstheelements7563142inincreasingorder.Drawfigures.DiscreteMathematicTest(Uni