Phil105Exam2Spring2020Name:__________________________Forthisexam,keepinmindthat:{&}Conjunctionsaretrueifandonlyifbothconjunctsaretrue.{V}Disjunctionsarefalseifandonlyifbothdisjunctsarefalse.{→}Conditionalsarefalseifandonlyiftheantecedentistrueandtheconsequentisfalse.{«}Biconditionalsaretrueifandonlyifbothsidesofthebiconditionalmatchintruthvalue.{~}Negationsaretrueifandonlyifwhatisnegatedisfalse. p q (p→q)
(p&q) (pVq) (p«q) ~p T T T T T T F T F F T F F F F T F T T F T F F F F T T T Providetruthtablesforthefollowingsentenceforms,thencirclethetermthatapplies. A B ((~AÚB)→A) CONTRADICTION TAUTOLOGY CONTINGENCY C D ((CÚ~D)Ú(CÚD)) CONTRADICTION TAUTOLOGY CONTINGENCY F G (F→(GÚ~G)) CONTRADICTION TAUTOLOGY CONTINGENCYProvidejointtruthtableforthefollowingpairofsentencesandcirclethephrasethatapplies. A B (~A→B)(AÚ~B) LOGICALLY EQUIVALENT NOT LOGICALLY EQUIVALENTDeterminewhetherornotthefollowingargumentformsarevalidusingtruthtables(circleone). A B Premise.(~A«B) Conclusion.(BÚA) VALID INVALID X Y Z Premise.(X→Y)
Premise.(Y«Z)Conclusion.(Z→X)
VALID INVALID A B C Premise.(C→A) Premise.(B→A) Premise.(CÚB) Conclusion.A VALID INVALIDUsingthekey{M:Thematchlights,S:Youstruckthematch}forthefollowingargument,(i)providetheformoftheargument,and(ii)useatruthtabletodeterminewhetherornottheargumentisvalid. Ifyoustrikethematch,thenthematchlights. Youstrikethematchanditdoesn’tlight. M S VALID INVALIDUsingthekey{O:ObamaisPresident,F:MichelleisFirstLady}forthefollowingargument,(i)providetheform,and(ii)useatruthtabletodeterminewhetherornottheargumentisvalid.P1)MichelleisnottheFirstLady.P2)NeitherisObamaPresident,norisMichelleFirstLady.C)IfMichelleisnottheFirstLady,thenObamaisnotthePresident. F O VALID INVALIDUsingthekey{R:ourcarwillrun,G:ourcarhasgasoline}forthefollowingargument,(i)providetheform,and(ii)useatruthtabletodeterminewhetherornottheargumentisvalid.P1)Ifourcardoesn’thavegasoline,itwon’trun.P2)Ourcarhasgasoline.C)Ourcarwillrun. G R VALID INVALIDUsingthefollowinginterpretation: theeconomyimproves consumersincreaseborrowing consumerspendingfalls unemploymentrises thereisahousingboom taxesareraised governmentspendingincreases stockpriceswillfall morejobswillbecreated interestrateswillriseTranslatethefollowingEnglishsentencesintoSL: Theeconomyimproves,butunemploymentrises. Theeconomyimprovesifbothtaxesaren’traisedandstockpricesdon’tfall. Governmentspendingincreases,andifmorejobsarecreatedthenwilltherebeahousingboom. Consumerspendingdoesnotfalliftheyincreaseborrowing,butunemploymentstillrises. Thereisahousingboomonlyifbothgovernmentspendingandconsumerborrowingincreases. Stockpriceswillfallifandonlyifconsumersdon’tincreaseborrowing.
PhilPhil105Exam2Spring2020