IntroductionmtomFormalmLogicmwithmPhilosophicalmApplicationsm
Instructor’smManualm
Chapterm2m
m
m
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Contentsm
Chapterm2mSummary m......................................................................................................................................m3m
Chapterm2mKey mTermsm.....................................................................................................................................m4m
Chapterm2mInstructormTestmBankm.....................................................................................................................m5
m
Chapterm1mMultiplemChoicem........................................................................................................................m5m
Sectionm2.1m.............................................................................................................................................m5m
Sectionm2.2m...........................................................................................................................................m10m
Sectionm2.3m...........................................................................................................................................m11m
Sectionm2.4m...........................................................................................................................................m14m
Sectionm2.5m...........................................................................................................................................m19m
Sectionm2.6m...........................................................................................................................................m22m
Sectionm2.7m...........................................................................................................................................m25m
Chapterm2mTraditionalm..............................................................................................................................m30m
Sectionm2.1m...........................................................................................................................................m30m
Sectionm2.2...............................................................................................................................................m31m
Sectionm2.3m...........................................................................................................................................m32m
Sectionm2.4m...........................................................................................................................................m33m
Sectionm2.5m...........................................................................................................................................m40m
Sectionm2.6m...........................................................................................................................................m45m
Sectionm2.7m...........................................................................................................................................m52m
m
m
m
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Chapterm2m-mPropositionalmLogic:mSyntaxmandmSemanticsm
m
Chapterm2mSummary:m
m
Propositionalmlogicmismthemlogicmof mpropositionsmandmtheirminferentialmrelations.m
m
Ampropositionmismamstatement,moftenmexpressedmbymamdeclarativemsentence,mwhichmhasmamtr
uthmvalue.mm
m
PLmismthemformalmobjectmlanguagemof mpropositionalmlogic.m
m
Themsyntaxmof mPLmspecifiesmitsmvocabulary mandmrulesmformmakingmformulas.m
, m
Themvocabulary mof mPLmincludesmuppercasemletters,mfivemoperators—
mtildem(~),mdotm(•),mvelm(˅),m
horseshoem(⊃),mtriple-barm(≡)—andmpunctuationmmarksm(),m[],m{}.m
m
Logicalmoperatorsmaremtoolsmformcombiningmpropositionsmormterms.mm
m
Unary moperatorsmapply monly mtomamsinglemproposition.mThey mnevermrelatemormconnectmtwomp
ropositions.m
Negation,m~,mismthemonly munary moperatorminmPL.m
m
Binary moperatorsmrelatemormconnectmtwompropositions.mAllmoperatorsmofmPL,mexceptmnegatio
n,marem
binary moperators.m
m
Negation,m~,mismthemlogicalmoperatormusedmtomtranslatem‘not’,m‘itmismnotmthemcasemthat’,m‘itmism
falsemthat’,m
andmrelatedmterms.mItmismthemonly munary moperator.mm
m
Conjunction,m•,mismthemlogicalmoperatormusedmtomtranslatem‘and’,m‘but’,mandmrelatedmterms.mIt
mismam
binary moperator.mThemformulasmjoinedmbymamconjunctionmaremcalledmconjuncts.mm
m
Disjunction,m˅,mismthemlogicalmoperatormusedmtomtranslatem‘or’,m‘unless’,mandmrelatedmterms.mI
tmismam
binary moperator.mThemformulasmjoinedmbymamdisjunctionmaremcalledmdisjuncts.mm
m
Materialmimplication,m⊃,mismthemlogicalmoperatormusedmtomtranslatemconditionals,m‘if m.m.m.mthe
nm.m.m.m
statements’,mandmrelatedmterms.mItmismambinary moperator.mThemformulamprecedingmthem⊃mism
calledmthem
antecedent;mthemformulamfollowingmthem⊃mismcalledmthemconsequent.mThemordermofmthemante
cedentmandm
consequentmismsignificant;mSm⊃mP mismnotmlogically mequivalentmtomP m⊃mS.mm
m
Thembiconditional,m≡,mismthemlogicalmoperatormusedmform‘if-and-only-
if’,mandmrelatedmterms.mItmismam
binary moperator.mThembiconditionalmismamconjunctionmof mamconditionalmwithmitsmconverse;m‘
Am≡mB’mism
shortmform‘(Am⊃mB)m•m(Bm⊃mA)’.mm
m
Formationmrulesmspecify mhow mtomcombinemthemvocabulary mof mamlanguagemintomwell-
formedmformulasm
,(wffs).m
m
Amwff,mormwell-
formedmformula,mismany mlogicalmsymbolmormstringmof msymbolsmthatmaremconstructedm
properly.mAmwff mismanalogousmtomamgrammatically mcorrectmsentence.m
m
PLmhasmfourmformationmrules.mPL1:mAmsinglemcapitalmEnglishmlettermismamwff.mPL2:mIf mαmismam
wff,msomism
~α.mPL3:mIfmαmandmβmaremwffs,mthenmsomare:m(αm•mβ),m(αm˅mβ),m(αm⊃mβ),mandm(αm≡mβ).mPL4:mT
hesemaremthem
only mwaysmtommakemwffs.m
m
Anmatomicmformulamof mPLmismany mwffmformedmby mamsinglemusemof mPL1:mamsinglemcapitalmEngl
ishmletter.m
m
Amcomplexmformulamof mPLmismamwff mformedminmanymway mbesidesmamsinglemusemofmPL1.mm
m
Themmainmoperatormismthemlastmoperatormaddedmtomamwffmaccordingmtomthemformationmrules.
mm
m
Themsemanticsmof mPLmspecifiesmthemrulesmforminterpretingmthemsymbolsmandmformulasmof mth
em
language.m
m
Bivalentmlogicmismamtwo-
valuedmlogic.mEvery mstatementmisminterpretedmasmeithermtruemormfalse,mandmnotm
both.mThemlogicmof mPLmisminterpretedmasmbivalent.m
m
Compositionality mismamsemanticmprinciplemstatingmthatmthemmeaningmofmamcomplexmsentence
mism
determinedmby mthemmeaningsmof mitsmcomponentmparts.mThemlanguagemof mPLmismcomposition
al.m
m
m
Themtruthmvaluemof mamcomplexmpropositionmismthemtruthmvaluemof mitsmmainmoperator.m
m
Amtruthmtablemshowsmthemtruthmvaluemformamcomplexmpropositionmgivenmany mtruthmvaluesmof
mitsm
componentmpropositions.m
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m
Thembasicmtruthmtablemismamway mofmrepresentingmthemsemanticmrulesmgoverningmeachmoperat
, ormby m
showingmthemtruthmvaluemof mthemoperation,mgivenmanympossiblemdistributionmof mtruthmvalues
mof mthem
componentmpropositions.m
m
Negation,m~,misminterpretedmasmtruemwhenmthemformulamtomwhichmitmappliesmismfalse;mitmismin
terpretedmasm
falsemwhenmthemformulamtomwhichmitmappliesmismtrue.m
m
Conjunction,m•,misminterpretedmasmtruemonly mwhenmbothmconjunctsmaremtrue;motherwisemitmis
mfalse.m
m
Disjunction,m˅,misminterpretedmasmfalsemonly mwhenmbothmdisjunctsmaremfalse;motherwisemitmis
mtrue.m
m
Materialmimplication,m⊃,misminterpretedmasmfalsemonly mwhenmthemantecedentmismtruemandmthe
m
consequentmismfalse;motherwisemitmismtrue.m
m
Thembiconditional,m≡,misminterpretedmasmtruemwhenmthemcomponentmstatementsmsharemthems
amemtruthm
value,m(whenmthey marembothmtruemormbothmfalse);motherwisemitmismfalse.m
m
Amsufficientmconditionmismsomethingmadequatemormenoughm(thoughmnotmnecessarily mrequire
d)mform
somethingmelsemtomobtain.mInmammaterialmimplication,mthemtruthmof mthemantecedentmismthems
ufficientm
conditionmof mthemtruthmof mthemconsequent.m
m
Amnecessary mconditionmismsomethingmrequiredm(thoughmnotmnecessarily madequatemormenoug
h)mform
somethingmelsemtomobtain.mInmammaterialmimplication,mthemtruthmof mthemconsequentmismthemn
ecessarym
conditionmof mthemtruthmof mthemantecedent.m
m
Amtautology mismampropositionmthatmismtrueminmevery mrowmofmitsmtruthmtable.mThey maremthemlo
gicalmtruthsm
of mPL.m
m
Logicalmtruthsmarempropositionsmthatmaremtruemonmany minterpretation.m
m
Amcontingency mismampropositionmthatmismtrueminmsomemrowsmof mitsmtruthmtablemandmfalseminm
others.m
m
Instructor’smManualm
Chapterm2m
m
m
DOWNLOADmTHEmTestmBankmformIntroductionmtomFormalmLogicm1stmEdition
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Contentsm
Chapterm2mSummary m......................................................................................................................................m3m
Chapterm2mKey mTermsm.....................................................................................................................................m4m
Chapterm2mInstructormTestmBankm.....................................................................................................................m5
m
Chapterm1mMultiplemChoicem........................................................................................................................m5m
Sectionm2.1m.............................................................................................................................................m5m
Sectionm2.2m...........................................................................................................................................m10m
Sectionm2.3m...........................................................................................................................................m11m
Sectionm2.4m...........................................................................................................................................m14m
Sectionm2.5m...........................................................................................................................................m19m
Sectionm2.6m...........................................................................................................................................m22m
Sectionm2.7m...........................................................................................................................................m25m
Chapterm2mTraditionalm..............................................................................................................................m30m
Sectionm2.1m...........................................................................................................................................m30m
Sectionm2.2...............................................................................................................................................m31m
Sectionm2.3m...........................................................................................................................................m32m
Sectionm2.4m...........................................................................................................................................m33m
Sectionm2.5m...........................................................................................................................................m40m
Sectionm2.6m...........................................................................................................................................m45m
Sectionm2.7m...........................................................................................................................................m52m
m
m
m
DOWNLOADmTHEmTestmBankmformIntroductionmtomFormalmLogicm1stmEdition
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Chapterm2m-mPropositionalmLogic:mSyntaxmandmSemanticsm
m
Chapterm2mSummary:m
m
Propositionalmlogicmismthemlogicmof mpropositionsmandmtheirminferentialmrelations.m
m
Ampropositionmismamstatement,moftenmexpressedmbymamdeclarativemsentence,mwhichmhasmamtr
uthmvalue.mm
m
PLmismthemformalmobjectmlanguagemof mpropositionalmlogic.m
m
Themsyntaxmof mPLmspecifiesmitsmvocabulary mandmrulesmformmakingmformulas.m
, m
Themvocabulary mof mPLmincludesmuppercasemletters,mfivemoperators—
mtildem(~),mdotm(•),mvelm(˅),m
horseshoem(⊃),mtriple-barm(≡)—andmpunctuationmmarksm(),m[],m{}.m
m
Logicalmoperatorsmaremtoolsmformcombiningmpropositionsmormterms.mm
m
Unary moperatorsmapply monly mtomamsinglemproposition.mThey mnevermrelatemormconnectmtwomp
ropositions.m
Negation,m~,mismthemonly munary moperatorminmPL.m
m
Binary moperatorsmrelatemormconnectmtwompropositions.mAllmoperatorsmofmPL,mexceptmnegatio
n,marem
binary moperators.m
m
Negation,m~,mismthemlogicalmoperatormusedmtomtranslatem‘not’,m‘itmismnotmthemcasemthat’,m‘itmism
falsemthat’,m
andmrelatedmterms.mItmismthemonly munary moperator.mm
m
Conjunction,m•,mismthemlogicalmoperatormusedmtomtranslatem‘and’,m‘but’,mandmrelatedmterms.mIt
mismam
binary moperator.mThemformulasmjoinedmbymamconjunctionmaremcalledmconjuncts.mm
m
Disjunction,m˅,mismthemlogicalmoperatormusedmtomtranslatem‘or’,m‘unless’,mandmrelatedmterms.mI
tmismam
binary moperator.mThemformulasmjoinedmbymamdisjunctionmaremcalledmdisjuncts.mm
m
Materialmimplication,m⊃,mismthemlogicalmoperatormusedmtomtranslatemconditionals,m‘if m.m.m.mthe
nm.m.m.m
statements’,mandmrelatedmterms.mItmismambinary moperator.mThemformulamprecedingmthem⊃mism
calledmthem
antecedent;mthemformulamfollowingmthem⊃mismcalledmthemconsequent.mThemordermofmthemante
cedentmandm
consequentmismsignificant;mSm⊃mP mismnotmlogically mequivalentmtomP m⊃mS.mm
m
Thembiconditional,m≡,mismthemlogicalmoperatormusedmform‘if-and-only-
if’,mandmrelatedmterms.mItmismam
binary moperator.mThembiconditionalmismamconjunctionmof mamconditionalmwithmitsmconverse;m‘
Am≡mB’mism
shortmform‘(Am⊃mB)m•m(Bm⊃mA)’.mm
m
Formationmrulesmspecify mhow mtomcombinemthemvocabulary mof mamlanguagemintomwell-
formedmformulasm
,(wffs).m
m
Amwff,mormwell-
formedmformula,mismany mlogicalmsymbolmormstringmof msymbolsmthatmaremconstructedm
properly.mAmwff mismanalogousmtomamgrammatically mcorrectmsentence.m
m
PLmhasmfourmformationmrules.mPL1:mAmsinglemcapitalmEnglishmlettermismamwff.mPL2:mIf mαmismam
wff,msomism
~α.mPL3:mIfmαmandmβmaremwffs,mthenmsomare:m(αm•mβ),m(αm˅mβ),m(αm⊃mβ),mandm(αm≡mβ).mPL4:mT
hesemaremthem
only mwaysmtommakemwffs.m
m
Anmatomicmformulamof mPLmismany mwffmformedmby mamsinglemusemof mPL1:mamsinglemcapitalmEngl
ishmletter.m
m
Amcomplexmformulamof mPLmismamwff mformedminmanymway mbesidesmamsinglemusemofmPL1.mm
m
Themmainmoperatormismthemlastmoperatormaddedmtomamwffmaccordingmtomthemformationmrules.
mm
m
Themsemanticsmof mPLmspecifiesmthemrulesmforminterpretingmthemsymbolsmandmformulasmof mth
em
language.m
m
Bivalentmlogicmismamtwo-
valuedmlogic.mEvery mstatementmisminterpretedmasmeithermtruemormfalse,mandmnotm
both.mThemlogicmof mPLmisminterpretedmasmbivalent.m
m
Compositionality mismamsemanticmprinciplemstatingmthatmthemmeaningmofmamcomplexmsentence
mism
determinedmby mthemmeaningsmof mitsmcomponentmparts.mThemlanguagemof mPLmismcomposition
al.m
m
m
Themtruthmvaluemof mamcomplexmpropositionmismthemtruthmvaluemof mitsmmainmoperator.m
m
Amtruthmtablemshowsmthemtruthmvaluemformamcomplexmpropositionmgivenmany mtruthmvaluesmof
mitsm
componentmpropositions.m
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m
Thembasicmtruthmtablemismamway mofmrepresentingmthemsemanticmrulesmgoverningmeachmoperat
, ormby m
showingmthemtruthmvaluemof mthemoperation,mgivenmanympossiblemdistributionmof mtruthmvalues
mof mthem
componentmpropositions.m
m
Negation,m~,misminterpretedmasmtruemwhenmthemformulamtomwhichmitmappliesmismfalse;mitmismin
terpretedmasm
falsemwhenmthemformulamtomwhichmitmappliesmismtrue.m
m
Conjunction,m•,misminterpretedmasmtruemonly mwhenmbothmconjunctsmaremtrue;motherwisemitmis
mfalse.m
m
Disjunction,m˅,misminterpretedmasmfalsemonly mwhenmbothmdisjunctsmaremfalse;motherwisemitmis
mtrue.m
m
Materialmimplication,m⊃,misminterpretedmasmfalsemonly mwhenmthemantecedentmismtruemandmthe
m
consequentmismfalse;motherwisemitmismtrue.m
m
Thembiconditional,m≡,misminterpretedmasmtruemwhenmthemcomponentmstatementsmsharemthems
amemtruthm
value,m(whenmthey marembothmtruemormbothmfalse);motherwisemitmismfalse.m
m
Amsufficientmconditionmismsomethingmadequatemormenoughm(thoughmnotmnecessarily mrequire
d)mform
somethingmelsemtomobtain.mInmammaterialmimplication,mthemtruthmof mthemantecedentmismthems
ufficientm
conditionmof mthemtruthmof mthemconsequent.m
m
Amnecessary mconditionmismsomethingmrequiredm(thoughmnotmnecessarily madequatemormenoug
h)mform
somethingmelsemtomobtain.mInmammaterialmimplication,mthemtruthmof mthemconsequentmismthemn
ecessarym
conditionmof mthemtruthmof mthemantecedent.m
m
Amtautology mismampropositionmthatmismtrueminmevery mrowmofmitsmtruthmtable.mThey maremthemlo
gicalmtruthsm
of mPL.m
m
Logicalmtruthsmarempropositionsmthatmaremtruemonmany minterpretation.m
m
Amcontingency mismampropositionmthatmismtrueminmsomemrowsmof mitsmtruthmtablemandmfalseminm
others.m
m
