Question

The compound statement $(-(P\wedge Q))\vee ((-P)\wedge Q)\Rightarrow ((-P)\wedge (-Q))$ is equivalent to

• A. $((\sim P)\vee Q)\wedge ((\sim Q)\vee P)$
• B. $(\sim Q)\vee P$
• C. $((-P)\vee Q)\wedge (-Q)$
• D. $(-P)\vee Q$

Answer 1

Answer: (A)

Let $r=(\sim (P\wedge Q))\vee ((\sim P)\wedge Q);s=$ $((\sim P)\wedge (\sim Q))$

P	Q	$\sim (P\wedge Q)$	$(-P)\wedge Q$	r	s	$r\to s$
T	T	F	F	F	F	T
T	F	T	F	T	F	F
F	T	T	T	T	F	F
F	F	T	F	T	T	T

Option (A) : $((\sim P)\vee Q)\wedge ((\sim Q)\vee P)$
is equivalent to (not of only $P)\wedge ($ not of only $Q$ )
$=($ Both $P,Q)$ and (neither P nor $Q)$