Question

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

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

Answer 1

The correct option is C $\sim p$

Given Boolean expression is

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

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

$=\sim p\wedge \sim q\vee \sim p\wedge q$

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

$=\sim p$

Hence, option C is correct.