Question

The expression $\sim (p\vee q)\vee (\sim p\wedge q)$ is logically equivalent to

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

Answer 1

The correct option is A $\sim p$

$\sim (p\vee q)\vee (\sim p\wedge q)$
$=(\sim p\wedge \sim q)\vee (\sim p\wedge q)$
$=\sim p\wedge (\sim q\vee q)$
$=\sim p\wedge T$, where $T$ is true.
$=\sim p$