PHIL1006(Fall06)PS2ans

PHIL1006(Fall06)PS2ans - 1. (10 marks) True or false? /' @...

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Unformatted text preview: 1. (10 marks) True or false? /' @ Circle ’T' if the. statemenf 1.5 true. Circle ‘1‘“ if the statement is falsp; For this question. you. should (LSS'H'J'TLH that g: and w are WFFs of SL. @ F If 2,1! is inconsistent, then (,9 is not at tautology. T @ If 1;: is inconsistent then 9* does not entail Q. T ® "Kant. believed that" is a truth functional connective. T F “33:(Fm -—+ 03)" is a valid MPL WFF. T F If X is an inconsistent set of MPL WFFS, then no member of X entails a member of X. T ® If to entails w then so is consistent. T ® If so is a tautoiogieal conditional, then the consequent of (p is not inconsistent. T ® If X is an inconsistent, set. of MPL WFFs. then some member of X is not valid. @ F The following argument can he shown to be valid in SL: “If everyone is hungry, then Slim is not hungry. Everyone is hungry. So, Slim is not hungry." (I) F q: is not. a “(PP of MP],. /10 [\J 2. (15 marks) Suppose that a new (me-plaice mnner-i ive ‘53". and a new two—place connective ‘#' are added to SL. You are informed that: ‘((A#B) —> @A)‘ is a tautology @A' does not. entail '(A#B)‘ “(A#B)' does not. entail “1198‘ ‘©A' is contingent ‘@A’ does not entail '(A V A)‘ Fill in the truth tables for '#' and Circie ‘T’ if the staining-mt 1.5: tT‘ur. (Ti-mute ‘F‘ if the statement is false: ‘(@A&B)’ is contingent “El/i. (A —-’ B) l: B‘ is a valid sequent. ‘(B#A)' is logically equivalent to ‘( B&:A}'. ‘(@A#'-@B)‘ does not entail ‘(B V A)‘. [15 3. (10 marks} For each of the foiiomsing: Circle “histology” if it "is a. [rVFF .0th that 1-3 a mummy?)- C’ircie "contingent" if it is rt contingent WFF of SL. Circle "inconsistent" if it is rm. inconsistent [II/"FF of SL. ()thef'wise‘ don't circte anything. (A <—> —> A}; tautology r nntingi-s 1t inconsistent ({A v (Beam) —» (A v 0)) t@' contingent inconsistent ((A8; at B) v (AS.an tautology cm@nt inconsistent ((A& ~ A) V (B V mBD tat®y contingent inconsistent ((24 H t”) —> (51 —' 0)) tau®gy contingent. inconsistent. \ ( B —, (A —s 8)) ta@y contingent inconsistent (A H {CM/1 V B)» tautology cit inconsistent (NF H AVA” tautology cc ingc it inconsistent E ((A —> B) V (B a A)) ty contingent inconsistent ({A <—> B) ——> {(A V (3') <—r (A&("))) tautology con inconsistent I miss??? odd/mark. _, “i “ I m3; mes/r») f -—] J@ j” 4. (15 marks) Tr‘amiate the foiiowrng statements and arguments into MPL. Preserve as much structure as possibirr. Use the follow-n9 tmn.sia.t-io-n scheme: a: Aaron 1'): Barbara Fx: x is friendly Gx: x is greedy (a) If Aaron and Berber-c1. are bot I1 greedy, then someone is friendly. __ Dori-nah 3 All Atrium , (( Gar-2x65» 9m) (b) If everyone is greedy, then sorrieone is. DMWX : A” AflMm (iix For *—> 3x5 X) (0) Aaron and Barbara are both greedy only if at least one of the two is not friendly. ((6s?~65)~—‘>(4F1\/AB)) (d) If everyone is greedy then Barbara is greedy. If someone is greedy, then he is friendly. But. Aaron is neither greedy nor friendly. So either every greedy person is not greedy or Aaron is friendly be mag ,' Air/nan,» , (Mr A; an, seam, (A 6’02; Ara) tag/46m as) v H) (e) Barbara is greedy but. not friendly. Aaron is both friendly and greedy. Therefore, not everyone who is greedy is friendiy. Démwjfl U9” Afl/Wf I (St 2 As) ,( row: A M We) /15 :3. (10 marks) {3 there on intern-vetotion under urn-inn att the fottoioing MPL WFFs are true? If yes, then gi-oe one such. intRip-rotation. If no. exptoin why there is no and; interpretation. ~EI:I:{A:L'&B.1;} Mir N (Am —> NEH) {4" Mink-74 367$ 4; X ’59me VCJT(~BJ: V ~03?) N 33:01: '0 Al 0ft 5 _ PI £551; If M3930 two/to) i *3?! /10 6. (10 marks) Write down 4 MPL WFFs which. are each consistent. but where there is no interpreta- tzon under ‘tflt';;tl‘??10?‘€ it}: I : :e WFFS is true. 3 f6 M a,” a” U j!» tom/e14 21:? {AS/— mt (Fa fist—i ) 4m Mam / 3 7m flfififi) ( 42% 3 AH) /10 If new}: minnow). 7". (10 1'narks) Give a consistent MPL L'L-WF wit-mo. 't.‘~' foise under every interpretation which contains fess than 4' elements in its domain. E“ x a a a {Ext—(<23) 21 9x( 5x3'4/LX'»EJX(TExX/fix)) 7‘ 9X (“taxi-Ag”) /10 6 8. ([0 marks) S “i Gi‘h‘f? an rnfim'premfixJo-n n-n.rfl:—:-r whrlr'h. " 'v’a:(H 1:84: hr) " is fnise and iV$HJII —> Gm] " is firm: I \ b3 mg“) .L flflf‘fl-‘UL/S HAL )t f3 (3.. Auman Em -'« X ’3 a nme/ /10 9. (10 marks) :2 @ GIL-ye nn MPL WFF' that as Iogirmffiy equivalent to each, of the following WFFs. Your answer must wi-ncindr: an r:.-z:rsr‘.ennm£ qnnnnfier if the origrnnfl WFF contains a universal quantifier, and m versa. (MPL WFF -.,-9 r5 iogtcnfifly Frrg'nr'vanrnt {.0 MPL WFF 1,6: if and onfly fiftp entails 111 and 1p entails $0.) (a) ~Vm(H$\/G:r:) 27x 4 (Hm/6x) M 37x (“Mg/fix) 5" g‘AKAHy—yfix) (h) ~33:(~H:r:&t ~ Gm) fléx) or «3x- .«(rmzxm v (rt/Mm) 0r ran-Am a flax) 22 (An/am) (d) 3:3{Hx&(?rc) n VX A (ng‘th) m. ,f/X (AHX Vfléx) or "VX (Hx '3' Aéx) (9) HynyéLc ~ Fm 7/},«7 NM a}? 7M :3 07 (“mfiVM/‘K /10 ...
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PHIL1006(Fall06)PS2ans - 1. (10 marks) True or false? /' @...

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