Question

For any two statements $p$ and $q$, the statement $\sim\left(p \vee q\right) \vee \left(\sim p \wedge q\right)$ the is equivalent to

• A. $\sim p$
• B. $p$
• C. $q$
• D. $\sim q$

Answer 1

Answer: (A)

$\sim p$

Answer 2

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