Symbolic Logic Question Paper

Symbolic Logic

Course:Bachelor Of Arts In Psychology

Institution: Kenyatta University question papers

Exam Year:2010

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2010/2011
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ARTS
APH 200:
SYMBOLIC LOGIC

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DATE: TUESDAY 30TH NOVEMBER 2010
TIME: 8.00 A.M. - 10.00 A.M.

INSTRUCTIONS
Answer any Three Questions.

1.
Clearly explain the following concepts
i)
Modus Ponens
ii)
Logical Consequence
iii)
Modus Tollens
iv)
Reductio ad absurdum
v)
Conditional Proof
2.
Tautologies are unconditionally true statements? Explain.
3.
Use truth-tree technique to prove the validity of the following arguments
a)
P ? ? P , Q
( ? P ) ? Q ?
/ P ? ? Q

b)
P ? Q , P ? R , S ? ? Q ?
/
? P

c)
P ? Q / ? ? (Q ? )
P
4.
Translate the following sentences into predicate symbolism using a key of your own choice.
a)
George is a mechanic
b)
Peter is taller than Jack but shorter than James
c)
There is something liked by everybody
d)
If John loves himself then there is at least something he loves.
5.
Use the method of natural deduction to prove validity of the following arguments
a)
(P ? Q) ? (P ? R) ?
/
P

b)
(P ? Q)? ? Q ?
/
? P

c)
(? )
x Zx / ? ( y
? ) (Zy ?
)
Hy

d)
( x
? ) Ax / ? ( x
? ) ( Ax ? Ax )

6.
Clearly distinguish the following:
a)
Bound and free variables
b)
Closed and open sentences
c)
Existential and Universal Quantification
d)
Monadic and Polyadic predicates