May03 - UNIVERSITY OF TORONTO Faculty of Arts and Science...

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Unformatted text preview: UNIVERSITY OF TORONTO Faculty of Arts and Science APRIL/MAY EXAMINATIONS PHL245H1 S - P. Bali Duration: 2 hours No Aids Allowed General Instructions: (i) Please write all answers in the exam booklets provided. (ii) Use extra booklets for rough work, if necessary. (iii) Write legibly and in only non-erasable pen. PART A: SHORT ANSWER (3 x 3 = 9 marks! For each of the following statements, (i)indicate whether it is true or false, and (ii)clear1y explain your answer. 1. On the PL Square of Opposition, if an A—sentence is true then its corresponding 1— sentence must also be true. 2. If an argument of SL is truth-firnctionally valid, then the set consisting only of its premises and the negation of its conclusion is truth-functionally inconsistent. 3. Any two quantificationally false sentences are quantificationally equivalent. PART B: SD DERIVATIONS [12 marks! 1. Show that the following argument is valid in SD: (BEF)&(CDG) E ~(FvG) DDC (BvC)v(D&E) ~L Page 1 of 4 PART C: PLI TRANSLATIONS (4 x 4 = 16 marks! UD: everything Lx: x is logical Px: x is a person Tx: x is a time Sxyz: x is a student of y at z t: Tom 5: Susan Using the interpretation given above, translate the following into PLI: 1. Any logical person always has at least two teachers. 2. Except Tom and Susan, anyone who never has a teacher is illogical. Using the interpretation given above, translate the following into unambiguous English: 3. (Vx)(‘v’y)[[(Px & Py) & (Elz)(Tz & (Sxtz & Sytz))] D x=y ] 4. ~(Elx)[Px & (32)(Vy)[(Tz & Py) I) Syxz]] & (VX)(PX D(Ely)(§|z)[(Py & Tz) & Sxyz] ) PART D: PROPERTIES OF RELATIONS 14 x 3 = 12 marks} Assuming an unrestricted UD, for each of the following relations, state (i) whether it is transitive, intransitive, or non-transitive; (ii) whether it is symmetrical, asymmetrical, or non-symmetrical; and (iii) whether it is reflexive, irreflexive, or non-reflexive x is larger than or smaller than y x is larger than or as fast as y x is larger than or the same size as y x is the biological father of y .4>.‘”!‘-’f" Page 2 of 4 PART E: PLI SEMANTICS: EXPLANATIONS {13 marks! 1. Explain why the following sentences are quantificationally equivalent: ~ [ (3x)Px 3 (Vz)(sz v Hbz) ] ~ (Vw) (Pw 3 (Vx) (Gbx v be)) PART F: PLI SEMANTICS: INTERPRETATION S 12 x 5 = 10 marks} 1. Provide an interpretation to show that the following is not quanitificationally valid: (Vy)(Vx)(Py 3 CW) (3x)Cxx (3x) ~ Cxx 2. Provide an interpretation to show that the following is not quantificationally true: ~ ~ ~[(Vx)(Ely)( x = y & ( Mx & Sx ))1 PART G: PLI TRUTH-FUNCTIONAL EXPANSION S 18 marks) 1. Show that the following sentences are not quantificationally equivalent by truth- functionally expanding them for a set of two constants, and then constructing an appropriate truth-table. (3x)(Px D (Vy)Gby) (3W)Pw :3 (Vz)sz Page 3 of 4 PART H: PD DERIVATIONS 18 marks) 1. Show that the following argument is valid in PD: (W) [ (3X) ~ ( EX & ZiX ) & ny1 ~ (Vx) ( Ex & Zix ) 2 ~ (Vx)Jx ~ (Vx) Jx PART I: PD+ DERIVATIONS (12 marks! 1. Show that the following derivability claim holds in PD+: {(Vx) [(3y)(Byb & nyb) :3 Fx], (320(be & anb)} :— (Vx)(be D ~Fx) :3 ~Bab TOTAL = 100 marks Page 4 of4 ...
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May03 - UNIVERSITY OF TORONTO Faculty of Arts and Science...

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