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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 nonerasable 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 truthﬁrnctionally valid, then the set consisting only of its
premises and the negation of its conclusion is truthfunctionally 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 nontransitive;
(ii) whether it is symmetrical, asymmetrical, or nonsymmetrical; and
(iii) whether it is reﬂexive, irreﬂexive, or nonreﬂexive 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 TRUTHFUNCTIONAL 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 truthtable. (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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This note was uploaded on 09/28/2009 for the course PHL 245 taught by Professor Bangu during the Winter '05 term at University of Toronto.
 Winter '05
 bangu

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