32 ~ Theory of Computer Science
3 P 1\ Q.
l' d
• - - IS ca,Je :
:. P
(a) Addition
(b) Conjunction
(c) Simplification
(d) Modus tollens
4. Modus ponens is
(a) -, Q
P=::;,Q
:. -, P
(b) -,P
PvQ
:. Q
(C) P
P=::;,Q
:. Q
(d) none of the above
5. -, P 1\ -, Q 1\ R is a minterm of:
(a) P v Q
(b) -, P 1\ -, Q 1\ R
(c) P 1\ Q 1\ R 1\ S
(d) P 1\ R
6. Find the truth value of P ~ Q if the truth values of P and Q are F and
T respectively.
7. For \vhat truth values of P. Q and R, the truth value of (P ~ Q) ~ R
is F?
(P, Q, R have the truth values F, T, F or F, T, T)
8. If P, Q. R have the truth values F, T, F, respectively, find the truth
value of (P ~ Q) v (P ~ R).
9. State universal generalization.
10. State existential instantiation.
EXERCISES
1.1 \Vhich of the following sentences are propositions?
(a) A tdangle has three sides.
(b) 11111 is a prime numbel:.
(c) Every dog is an animal.
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