PHL245 Test 1

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Jaqueline Brunning

TEST #1 PH[245F:ModernSymbolic Logic UniversitofTorontoatMississauga ProfessorfBrunning o{**, Februarylt,z|LL \ ) LastName: Flw*al I f \t FirsName: Ju:"#rtKA Student#: t?63?nl {"rt Part I symbolizeeachof the following sentenceon the basortnJscheme of abbreviatiothat accompaniit.(3pointeach30 pointtotalJ 1,. If taareraised,ththeeconomywilimproveif tstock marketissteady. taxesareraised;the economy-will improve; R: [p: e: thestockmarketisteadYJ ,-/-" ? + K-+ Q 2' If taxesraisedandthe stomarketissteadthenthe economywill improveunlesstheovernmentdoesnoincrease spending[P:axesarraisedQ:thestockmarkeissteadyR: theconomywill improveS: thevernmentincreases ;pendinB). lftte -? V,*9) [n D 1/e ,d W ffir PartI (continued) 3. Eithethegovernment erectstradebarriersdothercountries retaliaor theovernment bothgrantssubsidie!odomestic produceanddoesnot find new sourcesofrevenue.u'pt:he governmenterectstradebarriersQ:othercountriesretaliate; R:thegovernmentgrantssubsidieso domesticroduce; S:the governmentfindsnewsources ofrevenueJ u cu! € Irn 4. Thedollarwill fall if stockmarketdonotincrease; otherwisit won't.Pthe dollarilfall; stock prlces Q: ^,/L ) n*n ftdal -)r &Un -4 nt t{>'|u - l l n tr' 'tt'-' Assuming that foreignnks,who areeagerto keeptheir currenciestrong,restraineir interventiothecurrency markets,thenthe dollarill fall andinflcontinueassuming thatthe centrabankdoesnot intervene.Pforeignbanks restraitheir interventiohin the currencymarkQ:foreign banksare eagertokeeptheircurrenciestrong; R:the dollarwill fall; S:inflatwill continue;thecentralbankwill interveneJ q ^ P 'rtz , \/ f1 L/ If neitherAlfrednor Maryisiltythenthejudgehasmadea seriousmistakeon the other hand,atleasoneofthemis guiltytheneitherSmithis anaccompliceor hasmisleadthe judge.[P:lfredisguiltyQ:Mary isguiltyR:thejudgehas madea serioumistake;S:Smithisanaccomplice;T:Smithhas '-tl- r \ A - l * i - . -+R r'I I I I / A [t rvq)) . -/l / @, 2/e \,2 K L- 7 Part Ifcontinued) 7.The governmenwill not rig electionlyif it isanteed victorandit isn'taranteevictory unlessthe;,the ' polls (P: governmEhtwill majoritvotenorthe areright. the rig theelection;Q:thegovernmentisguaranteedvictory;R:the -vR An'tS reMinist but didnotwin a ,ill not dthatboththe esnot fa slow.P:thePrime will erec reMinisterwas i elected; LmajorityyS:the / ls; T:tht ./ '*R ^- r \\ | t-/ A I t t 9. Theburglarywasaninsideobandthe thief knthe combinatioonlyif neitherthekwasforcednorthewindow broken,assuminthathethiefidn'steathekey(P:the burglarywasaninsideob;Q:thethief knthe combination; R:the windowwas lockwasforced;S:the broken;T:thethief stolethekey) (rt *") -R ru$ l-:-: A 10.Theauthorwill winprizeusin casboth theaudienceloves theplayandthe criticsot ignoreit,videdthatubliciis neitheexpensivenor adver[P:heauthorwilwin aprizeQ: theaudienclovesthelay;R:thecriticsnot ignorethelay; S:publiciis expensive;T:bliciisadverse) r -1r ,/ ( ^.s n ",rJ -,> ( P s* (=Q nR]_,f " 3le \ / ^ ) '| (?'- ffi Part II Construct an abbreviated derivation for eachofthe following argurnents.Do Nor usetheorems. (10points each:50 poinftotal] 1. Rn[-S-+-QJ oR<>PnQ .'.PnS l Slonr.': P A,g & D. -6-Jl cf /-D) I l 3 A ) ) ' ? ( 4' K ' l 2 3-- rl> K - > ( f n l e B C t S ; ' \ Pt .ws f n n P Q , s c rI t a - b . FwA tID r\;$l {.?. ^/s s!3 7,. -) .- p 0 ! * , f,r S q fl -) q tsr il ,-q t l t" t& l , ( ** l n r ) l i t 3 - fr {Pne} \ l l { L \ , V [ l t v Ir+ f n q " 1 2 ;\3 t l r |. 1; + t ft r F n tr \g\9"!. t b - '-/ # Ia-.) w 3 4/e vu ffi PartII fcontinued) -R+-(PvQ) -tavR)vS+[P+SJ 2. .'. '_{j.. i vIevrJv$ *:] [c> 16 ] L '3t^"ur": [fl-**l__ p c h €ft r[& g ftd" uR") v
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