Question

$\sim(p \vee q) \vee (\sim p \land q)$ is logically equivalent to

• A. ~p
• B. p
• C. q
• D. ~q

Answer 1

Answer: (A)

~p

Answer 2

$\sim(p \vee q) \vee (\sim p \vee q))$

$\equiv (\sim p\mspace{6mu} \land \sim q) \vee (\sim p \land q$)

$\equiv \mspace{6mu}\sim p \land (\sim q \vee q) \equiv \mspace{6mu}\sim p$.