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)

$((\sim P) \vee Q) \wedge((\sim Q) \vee P)$

Answer 2

Let r=(∼(P∧Q))∨((∼P)∧Q);s= ((∼P)∧(∼Q))

P	Q	∼(P∧Q)	(−P)∧Q	r	s	r→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) : ((∼P)∨Q)∧((∼Q)∨P)
is equivalent to (not of only P)∧( not of only Q )
=( Both P,Q) and (neither P nor Q)