discrete mathematics for new technology second edition - garnier , taylor

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1、DiscreteMathematicsforNewTechnologySecondEditionRowanGarnierandJohnTaylorUniversityofBrighton,UKInstituteofPhysicsPublishingBristolandPhiladelphiacIOPPublishingLtd2002Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans

2、,electronic,mechanical,photocopying,recordingorotherwise,withoutthepriorpermissionofthepublisher.MultiplecopyingispermittedinaccordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgencyunderthetermsofitsagreementwiththeCommitteeofVice-ChancellorsandPrincipals.BritishLibraryCa

3、taloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.ISBN0750306521LibraryofCongressCataloging-in-PublicationDataareavailableFirstEditionpublished1992FirstEditionreprinted1996,1997,1999CommissioningEditor:JamesRevillProductionEditor:SimonLaurensonP

4、roductionControl:SarahPlentyCoverDesign:Fr´ed´eriqueSwistMarketingExecutive:LauraSerratricePublishedbyInstituteofPhysicsPublishing,whollyownedbyTheInstituteofPhysics,LondonInstituteofPhysicsPublishing,DiracHouse,TempleBack,BristolBS16BE,UKUSOffice:InstituteofPhysicsPublishing,ThePubl

5、icLedgerBuilding,Suite1035,150SouthIndependenceMallWest,Philadelphia,PA19106,USATypesetinLATEX2byText2Text,Torquay,DevonPrintedintheUKbyMPGBooksLtd,Bodmin,CornwallContentsContentsvPrefacetotheSecondEditionixPrefacetotheFirstEditionxiListofSymbolsxvChapter1:Logic11.1PropositionsandT

6、ruthValues11.2LogicalConnectivesandTruthTables21.3TautologiesandContradictions131.4LogicalEquivalenceandLogicalImplication151.5TheAlgebraofPropositions201.6MoreaboutConditionals241.7Arguments251.8PredicateLogic281.9ArgumentsinPredicateLogic38Chapter2:MathematicalProof442.1TheNatureo

7、fProof442.2AxiomsandAxiomSystems452.3MethodsofProof492.4MathematicalInduction63Chapter3:Sets733.1SetsandMembership733.2Subsets79viContents3.3OperationsonSets853.4CountingTechniques943.5TheAlgebraofSets983.6FamiliesofSets1053.7TheCartesianProduct1163.8TypesandTypedSetTheory128Chapter

8、4:Relations1484.1Re