Question

For the statements p and q, consider the following compound statements :
(a) $(\sim q\wedge (p\to q))\to \sim p$
(b) $((p\vee q)\wedge \sim p)\to q$
Then which of the following statements is correct?

• A. (a) and (b) both are not tautologies
• B. (a) and (b) both are tautologies
• C. (a) is a tautology but not (b)
• D. (b) is a tautology but not (a)

Answer 1

Answer: (B)

(A)

p	q	$\sim q$	$p\to q$	$\sim p$	$(\sim q\wedge (p\to q))$
T	T	F	T	F	F	T
T	F	T	F	F	F	T
F	T	F	T	T	F	T
F	F	T	T	T	T	T

(B)

p	q	$p\vee q$	$\sim p$	$(p\vee q)\wedge \sim p$
T	T	T	F	F	T
T	F	T	F	F	T
F	T	T	T	T	T
F	F	F	T	F	T

Both are tautologies