Symbolic Logic Question Paper

Symbolic Logic

Course:Bachelor Of Arts In Psychology

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ARTS

APH 200:
SYMBOLIC LOGIC

DATE: Thursday 24th December, 2009
TIME: 8.00 a.m ? 10.00 a.m
------------------------------------------------------------------------------------------------------------
INSTRUCTIONS:
Answer any THREE questions
SECTION A
1
a)
State and symbolically formulate the basic laws of thought.

b)
Use any methods to demonstrate that the laws of thought are tautological.

2.
a)
Using appropriate examples, explain some of the additives of Truth ?
Functional
logic.

b)
How does propositional natural deduction overcome the weakness in
2 (a)

c)
In which way is predicate natural deduction superior to propositional
calculus.
3.
Use the method of semantic tableaux to prove the validity of the following
argument
form:-
a)
P ? (R? S ),(R ? S ) ? Q ? P ? Q
b)
P ? Q, Q ? R, ? P ? R
c)
(Q ?T ) ? P,> Q ?T ? > P

4.
Use propositional natural deduction to prove the validity of the following
a)
P ?> Q ? > (P ? Q)
b)
> (P ? Q),> P ? Q ?Q
c)
(P ? Q)? (P ? R)? P ? (Q ? R)
5.
Prove the validity of the following theorems.

a)
Double negation P ? > > P

b)
De Morgans theorem > (P ? Q) ? (> P? > Q)
c)
Materials
Implication
(P ? Q) ? (> P ? Q)

6.
a)
Interpreting the letters ?F? and ?G? as the predicates ?is a frog? and ?is

green? respectively , formalize the

i)
If anything at all is a frog, then something is green.

ii)
If anything at all is a frog , then something is green

iii)
Only frogs are green
b)
Prove the validity of the following arguments
i)
x
? (Fx ? Gx)? > ( xFx
?
? Gx
?
)

ii)
x
? (?x ? Gx)? (?K ? Gh)? Md
iii)
y
? (Hy ? Fy ? Gy), zFz
?
? > xKxb
?

? x
? (Hx ? Gx)

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