IntroductiongtogFormalgLogicgwithgPhilosophicalgApplicationsg
Instructor’sgManualg
Chapterg2g
g
g
DOWNLOADgTHEgTestgBankgforgIntroductiongtogFormalgLogicg1stgEdition
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Contentsg
Chapterg2gSummaryg......................................................................................................................................g3g
Chapterg2gKeygTermsg.....................................................................................................................................g4g
Chapterg2gInstructorgTestgBankg..................................................................................................................... g5g
Chapterg1gMultiplegChoiceg........................................................................................................................ g5g
Sectiong2.1g.............................................................................................................................................g5g
Sectiong2.2g...........................................................................................................................................g10g
Sectiong2.3g...........................................................................................................................................g11g
Sectiong2.4g...........................................................................................................................................g14g
Sectiong2.5g........................................................................................................................................... g19g
Sectiong2.6g...........................................................................................................................................g22g
Sectiong2.7g...........................................................................................................................................g25g
Chapterg2gTraditionalg..............................................................................................................................g30g
Sectiong2.1g...........................................................................................................................................g30g
Sectiong2.2............................................................................................................................................... g31g
Sectiong2.3g...........................................................................................................................................g32g
Sectiong2.4g...........................................................................................................................................g33g
Sectiong2.5g........................................................................................................................................... g40g
Sectiong2.6g...........................................................................................................................................g45g
Sectiong2.7g...........................................................................................................................................g52g
g
g
g
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Chapterg2g-gPropositionalgLogic:gSyntaxgandgSemanticsg
g
Chapterg2gSummary:g
g
Propositionalglogicgisgtheglogicgofgpropositionsgandgtheirginferentialgrelations.g
g
Agpropositiongisgagstatement,goftengexpressedgbygagdeclarativegsentence,gwhichghasgagtruthgva
lue.gg
g
PLgisgthegformalgobjectglanguagegofgpropositionalglogic.g
g
ThegsyntaxgofgPLgspecifiesgitsgvocabularygandgrulesgforgmakinggformulas.g
g
,ThegvocabularygofgPLgincludesguppercasegletters,gfivegoperators—gtildeg(~),gdotg(•),gvelg(˅),g
horseshoeg(⊃),gtriple-barg(≡)—andgpunctuationgmarksg(),g[],g{}.g
g
Logicalgoperatorsgaregtoolsgforgcombininggpropositionsgorgterms.gg
g
Unarygoperatorsgapplygonlygtogagsinglegproposition.gTheygnevergrelategorgconnectgtwogpropo
sitions.g
Negation,g~,gisgthegonlygunarygoperatorgingPL.g
g
Binarygoperatorsgrelategorgconnectgtwogpropositions.gAllgoperatorsgofgPL,gexceptgnegation,gar
eg
binarygoperators.g
g
Negation,g~,gisgtheglogicalgoperatorgusedgtogtranslateg‘not’,g‘itgisgnotgthegcasegthat’,g‘itgisgfalsegt
hat’,g
andgrelatedgterms.gItgisgthegonlygunarygoperator.gg
g
Conjunction,g•,gisgtheglogicalgoperatorgusedgtogtranslateg‘and’,g‘but’,gandgrelatedgterms.gItgisgag
binarygoperator.gThegformulasgjoinedgbygagconjunctiongaregcalledgconjuncts.gg
g
Disjunction,g˅,gisgtheglogicalgoperatorgusedgtogtranslateg‘or’,g‘unless’,gandgrelatedgterms.gItgisgag
binarygoperator.gThegformulasgjoinedgbygagdisjunctiongaregcalledgdisjuncts.gg
g
Materialgimplication,g⊃,gisgtheglogicalgoperatorgusedgtogtranslategconditionals,g‘ifg.g.g.gtheng.g.g.g
statements’,gandgrelatedgterms.gItgisgagbinarygoperator.gThegformulagprecedinggtheg⊃gisgcalled
gtheg
antecedent;gthegformulagfollowinggtheg⊃gisgcalledgthegconsequent.gThegordergofgthegantecede
ntgandg
consequentgisgsignificant;gSg⊃gPgisgnotglogicallygequivalentgtogPg⊃gS.gg
g
Thegbiconditional,g≡,gisgtheglogicalgoperatorgusedgforg‘if-and-only-
if’,gandgrelatedgterms.gItgisgag
binarygoperator.gThegbiconditionalgisgagconjunctiongofgagconditionalgwithgitsgconverse;g‘Ag≡gB
’gisg
shortgforg‘(Ag⊃gB)g•g(Bg⊃gA)’.gg
g
Formationgrulesgspecifyghowgtogcombinegthegvocabularygofgaglanguagegintogwell-
formedgformulasg
(wffs).g
g
Agwff,gorgwell-
formedgformula,gisganyglogicalgsymbolgorgstringgofgsymbolsgthatgaregconstructedg
properly.gAgwffgisganalogousgtogaggrammaticallygcorrectgsentence.g
, g
PLghasgfourgformationgrules.gPL1:gAgsinglegcapitalgEnglishglettergisgagwff.gPL2:gIfgαgisgagwff,gsogi
sg
~α.gPL3:gIfgαgandgβgaregwffs,gthengsogare:g(αg•gβ),g(αg˅gβ),g(αg⊃gβ),gandg(αg≡gβ).gPL4:gThesegareg
theg
onlygwaysgtogmakegwffs.g
g
AngatomicgformulagofgPLgisganygwffgformedgbygagsinglegusegofgPL1:gagsinglegcapitalgEnglishglett
er.g
g
AgcomplexgformulagofgPLgisgagwffgformedginganygwaygbesidesgagsinglegusegofgPL1.gg
g
Thegmaingoperatorgisgtheglastgoperatorgaddedgtogagwffgaccordinggtogthegformationgrules.gg
g
ThegsemanticsgofgPLgspecifiesgthegrulesgforginterpretinggthegsymbolsgandgformulasgofgtheg
language.g
g
Bivalentglogicgisgagtwo-
valuedglogic.gEverygstatementgisginterpretedgasgeithergtruegorgfalse,gandgnotg
both.gTheglogicgofgPLgisginterpretedgasgbivalent.g
g
Compositionalitygisgagsemanticgprinciplegstatinggthatgthegmeaninggofgagcomplexgsentencegisg
determinedgbygthegmeaningsgofgitsgcomponentgparts.gTheglanguagegofgPLgisgcompositional.g
g
g
Thegtruthgvaluegofgagcomplexgpropositiongisgthegtruthgvaluegofgitsgmaingoperator.g
g
Agtruthgtablegshowsgthegtruthgvaluegforgagcomplexgpropositionggivenganygtruthgvaluesgofgitsg
componentgpropositions.g
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g
Thegbasicgtruthgtablegisgagwaygofgrepresentinggthegsemanticgrulesggoverninggeachgoperatorgb
yg
showinggthegtruthgvaluegofgthegoperation,ggivenganygpossiblegdistributiongofgtruthgvaluesgofgt
heg
componentgpropositions.g
g
Negation,g~,gisginterpretedgasgtruegwhengthegformulagtogwhichgitgappliesgisgfalse;gitgisginterpre
tedgasg
falsegwhengthegformulagtogwhichgitgappliesgisgtrue.g
g
Conjunction,g•,gisginterpretedgasgtruegonlygwhengbothgconjunctsgaregtrue;gotherwisegitgisgfalse
, .g
g
Disjunction,g˅,gisginterpretedgasgfalsegonlygwhengbothgdisjunctsgaregfalse;gotherwisegitgisgtrue.g
g
Materialgimplication,g⊃,gisginterpretedgasgfalsegonlygwhengthegantecedentgisgtruegandgtheg
consequentgisgfalse;gotherwisegitgisgtrue.g
g
Thegbiconditional,g≡,gisginterpretedgasgtruegwhengthegcomponentgstatementsgsharegthegsameg
truthg
value,g(whengtheygaregbothgtruegorgbothgfalse);gotherwisegitgisgfalse.g
g
Agsufficientgconditiongisgsomethinggadequategorgenoughg(thoughgnotgnecessarilygrequired)gfo
rg
somethinggelsegtogobtain.gIngagmaterialgimplication,gthegtruthgofgthegantecedentgisgthegsufficie
ntg
conditiongofgthegtruthgofgthegconsequent.g
g
Agnecessarygconditiongisgsomethinggrequiredg(thoughgnotgnecessarilygadequategorgenough)gf
org
somethinggelsegtogobtain.gIngagmaterialgimplication,gthegtruthgofgthegconsequentgisgthegnecess
aryg
conditiongofgthegtruthgofgthegantecedent.g
g
Agtautologygisgagpropositiongthatgisgtruegingeverygrowgofgitsgtruthgtable.gTheygaregtheglogicalgtr
uthsg
ofgPL.g
g
Logicalgtruthsgaregpropositionsgthatgaregtruegonganyginterpretation.g
g
Agcontingencygisgagpropositiongthatgisgtruegingsomegrowsgofgitsgtruthgtablegandgfalsegingothers.
g
g
Agcontradictiongisgagpropositiongthatgisgfalsegingeverygrowgofgitsgtruthgtable.g
g
Twogorgmoregpropositionsgareglogicallygequivalentgwhengtheyghavegthegsamegtruthgvaluesging
everyg
rowgofgtheirgtruthgtables.g
g
Twogpropositionsgaregcontradictorygwhengtheyghavegoppositegtruthgvaluesgingeverygrowgofgt
heirg
truthgtables.g
g
Twogorgmoregpropositionsgaregconsistentgwhengtheygaregtruegingatgleastgonegcommongrowgofg
theirg
Instructor’sgManualg
Chapterg2g
g
g
DOWNLOADgTHEgTestgBankgforgIntroductiongtogFormalgLogicg1stgEdition
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mynursytest.store
Contentsg
Chapterg2gSummaryg......................................................................................................................................g3g
Chapterg2gKeygTermsg.....................................................................................................................................g4g
Chapterg2gInstructorgTestgBankg..................................................................................................................... g5g
Chapterg1gMultiplegChoiceg........................................................................................................................ g5g
Sectiong2.1g.............................................................................................................................................g5g
Sectiong2.2g...........................................................................................................................................g10g
Sectiong2.3g...........................................................................................................................................g11g
Sectiong2.4g...........................................................................................................................................g14g
Sectiong2.5g........................................................................................................................................... g19g
Sectiong2.6g...........................................................................................................................................g22g
Sectiong2.7g...........................................................................................................................................g25g
Chapterg2gTraditionalg..............................................................................................................................g30g
Sectiong2.1g...........................................................................................................................................g30g
Sectiong2.2............................................................................................................................................... g31g
Sectiong2.3g...........................................................................................................................................g32g
Sectiong2.4g...........................................................................................................................................g33g
Sectiong2.5g........................................................................................................................................... g40g
Sectiong2.6g...........................................................................................................................................g45g
Sectiong2.7g...........................................................................................................................................g52g
g
g
g
DOWNLOADgTHEgTestgBankgforgIntroductiongtogFormalgLogicg1stgEdition
ggggggggggggggggggggggggggggggMarcus
mynursytest.store
Chapterg2g-gPropositionalgLogic:gSyntaxgandgSemanticsg
g
Chapterg2gSummary:g
g
Propositionalglogicgisgtheglogicgofgpropositionsgandgtheirginferentialgrelations.g
g
Agpropositiongisgagstatement,goftengexpressedgbygagdeclarativegsentence,gwhichghasgagtruthgva
lue.gg
g
PLgisgthegformalgobjectglanguagegofgpropositionalglogic.g
g
ThegsyntaxgofgPLgspecifiesgitsgvocabularygandgrulesgforgmakinggformulas.g
g
,ThegvocabularygofgPLgincludesguppercasegletters,gfivegoperators—gtildeg(~),gdotg(•),gvelg(˅),g
horseshoeg(⊃),gtriple-barg(≡)—andgpunctuationgmarksg(),g[],g{}.g
g
Logicalgoperatorsgaregtoolsgforgcombininggpropositionsgorgterms.gg
g
Unarygoperatorsgapplygonlygtogagsinglegproposition.gTheygnevergrelategorgconnectgtwogpropo
sitions.g
Negation,g~,gisgthegonlygunarygoperatorgingPL.g
g
Binarygoperatorsgrelategorgconnectgtwogpropositions.gAllgoperatorsgofgPL,gexceptgnegation,gar
eg
binarygoperators.g
g
Negation,g~,gisgtheglogicalgoperatorgusedgtogtranslateg‘not’,g‘itgisgnotgthegcasegthat’,g‘itgisgfalsegt
hat’,g
andgrelatedgterms.gItgisgthegonlygunarygoperator.gg
g
Conjunction,g•,gisgtheglogicalgoperatorgusedgtogtranslateg‘and’,g‘but’,gandgrelatedgterms.gItgisgag
binarygoperator.gThegformulasgjoinedgbygagconjunctiongaregcalledgconjuncts.gg
g
Disjunction,g˅,gisgtheglogicalgoperatorgusedgtogtranslateg‘or’,g‘unless’,gandgrelatedgterms.gItgisgag
binarygoperator.gThegformulasgjoinedgbygagdisjunctiongaregcalledgdisjuncts.gg
g
Materialgimplication,g⊃,gisgtheglogicalgoperatorgusedgtogtranslategconditionals,g‘ifg.g.g.gtheng.g.g.g
statements’,gandgrelatedgterms.gItgisgagbinarygoperator.gThegformulagprecedinggtheg⊃gisgcalled
gtheg
antecedent;gthegformulagfollowinggtheg⊃gisgcalledgthegconsequent.gThegordergofgthegantecede
ntgandg
consequentgisgsignificant;gSg⊃gPgisgnotglogicallygequivalentgtogPg⊃gS.gg
g
Thegbiconditional,g≡,gisgtheglogicalgoperatorgusedgforg‘if-and-only-
if’,gandgrelatedgterms.gItgisgag
binarygoperator.gThegbiconditionalgisgagconjunctiongofgagconditionalgwithgitsgconverse;g‘Ag≡gB
’gisg
shortgforg‘(Ag⊃gB)g•g(Bg⊃gA)’.gg
g
Formationgrulesgspecifyghowgtogcombinegthegvocabularygofgaglanguagegintogwell-
formedgformulasg
(wffs).g
g
Agwff,gorgwell-
formedgformula,gisganyglogicalgsymbolgorgstringgofgsymbolsgthatgaregconstructedg
properly.gAgwffgisganalogousgtogaggrammaticallygcorrectgsentence.g
, g
PLghasgfourgformationgrules.gPL1:gAgsinglegcapitalgEnglishglettergisgagwff.gPL2:gIfgαgisgagwff,gsogi
sg
~α.gPL3:gIfgαgandgβgaregwffs,gthengsogare:g(αg•gβ),g(αg˅gβ),g(αg⊃gβ),gandg(αg≡gβ).gPL4:gThesegareg
theg
onlygwaysgtogmakegwffs.g
g
AngatomicgformulagofgPLgisganygwffgformedgbygagsinglegusegofgPL1:gagsinglegcapitalgEnglishglett
er.g
g
AgcomplexgformulagofgPLgisgagwffgformedginganygwaygbesidesgagsinglegusegofgPL1.gg
g
Thegmaingoperatorgisgtheglastgoperatorgaddedgtogagwffgaccordinggtogthegformationgrules.gg
g
ThegsemanticsgofgPLgspecifiesgthegrulesgforginterpretinggthegsymbolsgandgformulasgofgtheg
language.g
g
Bivalentglogicgisgagtwo-
valuedglogic.gEverygstatementgisginterpretedgasgeithergtruegorgfalse,gandgnotg
both.gTheglogicgofgPLgisginterpretedgasgbivalent.g
g
Compositionalitygisgagsemanticgprinciplegstatinggthatgthegmeaninggofgagcomplexgsentencegisg
determinedgbygthegmeaningsgofgitsgcomponentgparts.gTheglanguagegofgPLgisgcompositional.g
g
g
Thegtruthgvaluegofgagcomplexgpropositiongisgthegtruthgvaluegofgitsgmaingoperator.g
g
Agtruthgtablegshowsgthegtruthgvaluegforgagcomplexgpropositionggivenganygtruthgvaluesgofgitsg
componentgpropositions.g
DOWNLOADgTHEgTestgBankgforgIntroductiongtogFormalgLogicg1stgEdition
ggggggggggggggggggggggggggggggMarcus
mynursytest.store
g
Thegbasicgtruthgtablegisgagwaygofgrepresentinggthegsemanticgrulesggoverninggeachgoperatorgb
yg
showinggthegtruthgvaluegofgthegoperation,ggivenganygpossiblegdistributiongofgtruthgvaluesgofgt
heg
componentgpropositions.g
g
Negation,g~,gisginterpretedgasgtruegwhengthegformulagtogwhichgitgappliesgisgfalse;gitgisginterpre
tedgasg
falsegwhengthegformulagtogwhichgitgappliesgisgtrue.g
g
Conjunction,g•,gisginterpretedgasgtruegonlygwhengbothgconjunctsgaregtrue;gotherwisegitgisgfalse
, .g
g
Disjunction,g˅,gisginterpretedgasgfalsegonlygwhengbothgdisjunctsgaregfalse;gotherwisegitgisgtrue.g
g
Materialgimplication,g⊃,gisginterpretedgasgfalsegonlygwhengthegantecedentgisgtruegandgtheg
consequentgisgfalse;gotherwisegitgisgtrue.g
g
Thegbiconditional,g≡,gisginterpretedgasgtruegwhengthegcomponentgstatementsgsharegthegsameg
truthg
value,g(whengtheygaregbothgtruegorgbothgfalse);gotherwisegitgisgfalse.g
g
Agsufficientgconditiongisgsomethinggadequategorgenoughg(thoughgnotgnecessarilygrequired)gfo
rg
somethinggelsegtogobtain.gIngagmaterialgimplication,gthegtruthgofgthegantecedentgisgthegsufficie
ntg
conditiongofgthegtruthgofgthegconsequent.g
g
Agnecessarygconditiongisgsomethinggrequiredg(thoughgnotgnecessarilygadequategorgenough)gf
org
somethinggelsegtogobtain.gIngagmaterialgimplication,gthegtruthgofgthegconsequentgisgthegnecess
aryg
conditiongofgthegtruthgofgthegantecedent.g
g
Agtautologygisgagpropositiongthatgisgtruegingeverygrowgofgitsgtruthgtable.gTheygaregtheglogicalgtr
uthsg
ofgPL.g
g
Logicalgtruthsgaregpropositionsgthatgaregtruegonganyginterpretation.g
g
Agcontingencygisgagpropositiongthatgisgtruegingsomegrowsgofgitsgtruthgtablegandgfalsegingothers.
g
g
Agcontradictiongisgagpropositiongthatgisgfalsegingeverygrowgofgitsgtruthgtable.g
g
Twogorgmoregpropositionsgareglogicallygequivalentgwhengtheyghavegthegsamegtruthgvaluesging
everyg
rowgofgtheirgtruthgtables.g
g
Twogpropositionsgaregcontradictorygwhengtheyghavegoppositegtruthgvaluesgingeverygrowgofgt
heirg
truthgtables.g
g
Twogorgmoregpropositionsgaregconsistentgwhengtheygaregtruegingatgleastgonegcommongrowgofg
theirg
