答案--离散数学及其应用英文版第7版.pdf

答案--离散数学及其应用英文版第7版.pdf

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1ANSRosen-2311TMHIA017-Rosen-v5.clsMay13,201110:

29AnswerstoOdd-NumberedExercisesCHAPTER1Section1.11.a）Yes,Tb）Yes,Fc）Yes,Td）Yes,Fe）Nof）No3.a）MeidoesnothaveanMP3player.b）ThereispollutioninNewJersey.c）2+1?

=3.d）ThesummerinMaineisnothotoritisnotsunny.5.a）Stevedoesnothavemorethan100GBfreediskspaceonhislaptopb）Zachdoesnotblocke-mailsfromJennifer,orhedoesnotblocktextsfromJenniferc）71113?

=999d）Dianedidnotrideherbike100milesonSunday7.a）Fb）Tc）Td）Te）T9.a）Sharkshavenotbeenspottedneartheshore.b）SwimmingattheNewJerseyshoreisallowed,andsharkshavebeenspottedneartheshore.c）SwimmingattheNewJerseyshoreisnotallowed,orsharkshavebeenspottedneartheshore.d）IfswimmingattheNewJerseyshoreisallowed,thensharkshavenotbeenspottedneartheshore.e）Ifsharkshavenotbeenspottedneartheshore,thenswimmingattheNewJerseyshoreisallowed.f）IfswimmingattheNewJerseyshoreisnotallowed,thensharkshavenotbeenspottedneartheshore.g）SwimmingattheNewJerseyshoreisallowedifandonlyifsharkshavenotbeenspottedneartheshore.h）SwimmingattheNewJerseyshoreisnotallowed,andeitherswimmingattheNewJerseyshoreisallowedorsharkshavenotbeenspottedneartheshore.（Notethatwewereabletoincorporatetheparen-thesesbyusingtheword“either”inthesecondhalfofthesentence.）11.a）pqb）pqc）pqd）pqe）pqf）（pq）（pq）g）qp13.a）pb）pqc）pqd）pqe）pqf）qpg）qp15.a）rpb）pqrc）r（qp）d）qpre）（q（rp）（rp）q）f）（pr）q17.a）Falseb）Truec）Trued）True19.a）Exclusiveor:

Yougetonlyonebeverage.b）Inclusiveor:

Longpasswordscanhaveanycombinationofsymbols.c）Inclusiveor:

Astudentwithbothcoursesisevenmorequal-ified.d）Eitherinterpretationpossible;atravelermightwishtopaywithamixtureofthetwocurrencies,orthestoremaynotallowthat.21.a）Inclusiveor:

Itisallowabletotakediscretemathematicsifyouhavehadcalculusorcomputerscience,orboth.Exclusiveor:

Itisallowabletotakediscretemathematicsifyouhavehadcalculusorcomputerscience,butnotifyouhavehadboth.Mostlikelytheinclusiveorisintended.b）Inclusiveor:

Youcantaketherebate,oryoucangetalow-interestloan,oryoucangetboththerebateandalow-interestloan.Exclusiveor:

Youcantaketherebate,oryoucangetalow-interestloan,butyoucannotgetboththerebateandalow-interestloan.Mostlikelytheexclusiveorisintended.c）Inclusiveor:

Youcanordertwoitemsfromcol-umnAandnonefromcolumnB,orthreeitemsfromcolumnBandnonefromcolumnA,orfiveitemsincludingtwofromcolumnAandthreefromcolumnB.Exclusiveor:

YoucanordertwoitemsfromcolumnAorthreeitemsfromcolumnB,butnotboth.Almostcertainlytheexclusiveorisintended.d）Inclusiveor:

Morethan2feetofsnoworwindchillbelow100,orboth,willcloseschool.Exclusiveor:

Morethan2feetofsnoworwindchillbelow100,butnotboth,willcloseschool.Certainlytheinclusiveorisintended.23.a）Ifthewindblowsfromthenortheast,thenitsnows.b）Ifitstayswarmforaweek,thentheappletreeswillbloom.c）IfthePis-tonswinthechampionship,thentheybeattheLakers.d）IfyougettothetopofLongsPeak,thenyoumusthavewalked8miles.e）Ifyouareworld-famous,thenyouwillgettenureasaprofessor.f）Ifyoudrivemorethan400miles,thenyouwillneedtobuygasoline.g）Ifyourguaranteeisgood,thenyoumusthaveboughtyourCDplayerlessthan90daysago.h）Ifthewaterisnottoocold,thenJanwillgoswimming.25.a）Youbuyanicecreamconeifandonlyifitishotout-side.b）Youwinthecontestifandonlyifyouholdtheonlywinningticket.c）Yougetpromotedifandonlyifyouhaveconnections.d）Yourmindwilldecayifandonlyifyouwatchtelevision.e）ThetrainrunslateifandonlyifitisadayItakethetrain.27.a）Converse:

“Iwillskitomorrowonlyifitsnowstoday.”Contrapositive:

“IfIdonotskitomorrow,thenitwillnothavesnowedtoday.”Inverse:

“Ifitdoesnotsnowtoday,thenIwillnotskitomorrow.”b）Converse:

“IfIcometoclass,thentherewillbeaquiz.”Contrapositive:

“IfIdonotcometoclass,thentherewillnotbeaquiz.”Inverse:

“Ifthereisnotgoingtobeaquiz,thenIdontcometoclass.”c）Converse:

“Apositiveintegerisaprimeifithasnodivisorsotherthan1anditself.”Contrapositive:

“Ifapositiveintegerhasadivisorotherthan1anditself,thenitisnotprime.”In-verse:

“Ifapositiveintegerisnotprime,thenithasadivisorotherthan1anditself.”29.a）2b）16c）64d）1631.a）ppppTFFFTFb）ppppTFTFTTc）pqqpq（pq）qTTFTTTFTTFFTFFTFFTTFd）pqpqpq（pq）（pq）TTTTTTFTFFFTTFFFFFFTS-1P1:

1ANSRosen-2311TMHIA017-Rosen-v5.clsMay13,201110:

29S-2AnswerstoOdd-NumberedExercisese）（pq）pqpqqpqp（qp）TTTFFTTTFFTFFTFTTFTTTFFTTTTTf）（pq）pqpqqp（qp）TTTTTTFFTTFTTFFFFTTT33.Forparts（a）,（b）,（c）,（d）,and（f）wehavethistable.pq（pq）（pq）（pq）（pq）（pq）（pq）（pq）（pq）（pq）（pq）TTFTFTTTFTFTTFFTTFTTFFFTTFTTForpart（e）wehavethistable.pqrprpqpr（pq）（pr）TTTFFTTFTTFFTTFTTFTFFFTTTFFFTFFFFTTTFFFFFTFTTFTTFFTTFTFTFFFTTTTF35.（pq）（pq）（pq）（pq）pqpqpq（pq）（pq）（pq）（pq）TTFFTTTTTFTTTFTTFTTTTTTTFFTFTFTT37.（pq）（pq）（pq）（pq）pqrp（qr）p（qr）（pr）（pr）（qr）（qr）TTTTTTTTTTTFFTTTTFTFTTTTFTTTFFTTTFFFFTTTTTTFFFTFTFTFTTFFTTTTTTFFFFTTTFTTP1:

1ANSRosen-2311TMHIA017-Rosen-v5.clsMay13,201110:

29AnswerstoOdd-NumberedExercisesS-339.（pq）pqrspqrs（rs）TTTTTTTTTTFTFFTTFTTFFTTFFTTTTFTTFTFTFTFFFTTFFTFFTTFFFFTFFTTTFTFFTTFFFTFTFTFFTFTFFFTFFFTTTTTFFTFTFFFFFTTFFFFFFTTT41.Thefirstclauseistrueifandonlyifatleastoneofp,q,andristrue.Thesecondclauseistrueifandonlyifatleastoneofthethreevariablesisfalse.ThereforetheentirestatementistrueifandonlyifthereisatleastoneTandoneFamongthetruthvaluesofthevariables,inotherwords,thattheydontallhavethesametruthvalue.43.a）BitwiseORis1111111;bitwiseANDis0000000;bitwiseXORis1111111.b）BitwiseORis11111010;bitwiseANDis10100000;bitwiseXORis01011010.c）BitwiseORis1001111001;bitwiseANDis0001000000;bitwiseXORis1000111001.d）BitwiseORis1111111111;bitwiseANDis0000000000;bitwiseXORis1111111111.45.0.2,0.647.0.8,0.649.a）The99thstatementistrueandtherestarefalse.b）Statements1through50arealltrueandstatements51through100areallfalse.c）Thiscannothappen;itisaparadox,showingthatthesecannotbestatements.Section1.21.ea3.g（r（m）（b）5.e（a（bp）r）7.a）qpb）qpc）qpd）qp9.Notconsistent11.Consistent13.NEWANDJER-SEYANDBEACHES,（JERSEYANDBEACHES）NOTNEW15.“IfIweretoaskyouwhethertherightbranchleadstotheruins,wouldyouansweryes?

”17Ifthefirstprofessordidnotwantcoffee,thenhewouldknowthatthean-swertothehostesssquestionwas“no.”Thereforethehostessandtheremainingprofessorsknowthatthefirstprofessordidwantcoffee.Similarly,thesecondprofessormustwantcoffee.Whenthethirdprofessorsaid“no,”thehostessknowsthatthethirdprofessordoesnotwantcoffee.19.AisaknightandBisaknave.21.AisaknightandBisaknight.23.AisaknaveandBisaknight.25.Aistheknight,Bisthespy,Cistheknave.27.Aistheknight,Bisthespy,Cistheknave.29.Anyofthethreecanbetheknight,anycanbethespy,anycanbetheknave.31.Nosolutions33.Inorderofde-creasingsalary:

Fred,Maggie,Janice35.Thedetectivecandeterminethatthebutlerandcookarelyingbutcannotdeter-minewhetherthegardeneristellingthetruthorwhetherthehandymanistellingthetruth.37.TheJapanesemanownsthezebra,andtheNorwegiandrinkswater.39.Onehonest,49corrupt41.a）（p（qr）b）（p）（q）（pr）43.prqpqrSection1.31.Theequivalencesfollowbyshowingthattheappropriatepairsofcolumnsofthistableagree.ppTpFpFpTppppTTTFTTTFFFFTFF3.a）pqpqqpTTTTTFTTFTTTFFFFb）pqpqqpTTTTTFFFFTFFFFFF5.（pq）pqrqrp（qr）pqpr（pr）TTTTTTTTTTFTTTFTTFTTTFTTTFFFFFFFFTTTFFFFFTFTFFFFFFTTFFFFFFFFFFFF7.a）Janisnotrich,orJanisnothappy.b）Carloswillnotbicycletomorrow,andCarloswillnotruntomorrow.c）Meidoesnotwalktoclass,andMeidoesnottakethebustoclass.d）Ibrahimisnotsmart,orIbrahimisnothardworking.9.a）pqpq（pq）pTTTTTFFTFTFTFFFTP1:

1ANSRosen-2311TMHIA017-Rosen-v5.clsMay13,201110:

29S-4AnswerstoOdd-NumberedExercisesb）pqpqp（pq）TTTTTFTTFTTTFFFTc）pqppqp（pq）TTFTTTFFFTFTTTTFFTTTd）pqpqpq（pq）（pq）TTTTTTFFFTFTFTTFFFTTe）pqpq（pq）（pq）pTTTFTTFFTTFTTFTFFTFTf）pqpq（pq）q（pq）qTTTFFTTFFTTTFTTFFTFFTFTT11.Ineachcasewewillshowthatifthehypothesisistrue,thentheconclusionisalso.a）Ifthehypothesispqistrue,thenbythedefinitionofconjunction,theconclusionpmustalsobetrue.b）Ifthehypothesispistrue,bythedefinitionofdisjunction,theconclusionpqisalsotrue.c）Ifthehypothesispistrue,thatis,ifpisfalse,thentheconclusionpqistrue.d）Ifthehypothesispqistrue,thenbothpandqaretrue,sotheconclusionpqisalsotrue.e）Ifthehypothesis（pq）istrue,thenpqisfalse,sotheconclusionpistrue（andqisfalse）.f）Ifthehypothesis（pq）istrue,thenpqisfalse,sopistrueandqisfalse.Hence,theconclusionqistrue.13.Thatthefourthcolumnofthetruthtableshownisidenticaltothefirstcolumnprovespart（a）,andthatthesixthcolumnisidenticaltothefirstcolumnprovespart（b）.pqpqp（pq）pqp（pq）TTTTTTTFFTTTFTFFTFFFFFFF15.Itisatautology.17.Eachoftheseistruepreciselywhenpandqhaveoppositetruthvalues.19.Thepropositionpqistruewhenpandqhavethesametruthval-ues,whichmeansthatpandqhavedifferenttruthvalues.Similarly,pqistrueinexactlythesamecases.There-fore,thesetwoexpressionsarelogicallyequivalent.21.Theproposition（pq）istruewhenpqisfalse,whichmeansthatpandqhavedifferenttruthvalues.Becausethisispreciselywhenpqistrue,thetwoexpressionsarelogi-callyequivalent.23.For（pr）（qr）tobefalse,oneofthetwoconditionalstatementsmustbefalse,whichhap-pensexactlywhenrisfalseandatleastoneofpandqistrue.Butthesearepreciselythecasesinwhichpqistrueandrisfalse,whichispreciselywhen（pq）risfalse.Becausethetwopropositionsarefalseinexactlythesamesituations,theyar