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Economics (200)
ECON 2P30 (6)
Lecture

Chapter2.pdf

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Department
Economics
Course
ECON 2P30
Professor
Lester Kwong
Semester
Winter

Description
TheTheoryofProofsLesterMKKwongDepartmentofEconomicsBrockUniversityVersion311RevisedSeptember202010Copyright2010LesterMKKwongDepartmentofEconomicsBrockUniversity500GlenridgeAveStCatharinesOntarioL2S3A1CanadaEmaillkwongbrockucaTel19056885550Ext5137ThisdocumentwastypesetwithAtheLTXDocumentationSystemusingtheXpicandtheMnSymbolpackagesYE1IntroductionGivenourdiscussionofpropositionsandtheuseofconnectivesandquantierstomakevalidpropositionalformsinthepreviouschapterthenextimportanttooltolearnisinestablishingthetruthfulnessofagivenpropositionForexampleonecouldclaimthatifaconsumerhaslocallynonsatiatedpreferencesthenWalraslawholdsThisisclearlyfromourpreviousdiscussionofpropositionallogicaconditionalsentencegivenbyPRwherePAconsumerhaslocallynonsatiatedpreferencesandRWalraslawholdsWeshouldalsoknowbynowthattheconditionalstatementisfalseonlywhentheantecedentistrueandtheconsequentisfalseThisonlyprovidesuswithinformationastowhenthepropositionalformitselfistrueorfalseandsaysnothingregardingtheactualstatementitselfAproofofthestatementthenwillpreciselybetheclaimtotherowsofthetruthtableforwhichthepropositionalformistrueInthisprocessofjusticationweareallowedtousepreviouslyprovedtheoremsaxiomsassumptionsdenitionstautologiesandthetheoremspremiseForexampleinestablishinganequilibriuminapricecompetitiongamebetweentwormsonecouldassertthestatementpporpp1212wherepisthepriceoeredbyrmiandbecorrectThisisduetothefactithatifweallowthepropositionRppthenwearemerelysuggesting12thetautologyRRSomeotherimportanttautologieswhichwillcomeinhandyare1AssociativityPQRPQRPQRPQR2DistributivityPQRPQPRPQRPQPR3ExcludedMiddlePP4DeMorgansLawsPQPQPQPQ1
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