Question

For any two statements $p$ and $q,$ the expression $\sim (p\vee q)\vee (\sim p\wedge q)$ is logically equivalent to

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

Answer 1

The correct option is B $\sim p$

$\sim (p\vee q)\vee (\sim p\wedge q)$
$\equiv (\sim p\wedge \sim q)\vee (\sim p\wedge q)$
$\equiv \sim p\wedge (\sim q\vee q)$
$\equiv \sim p\wedge T,$ where $T$ is tautology.
$\equiv \sim p$