Question

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

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

Answer 1

The correct option is D $\sim p\wedge \sim q$

$p\vee (\sim p\wedge q)$
$\Rightarrow (p\vee \sim p)\wedge (p\vee q)$
$\Rightarrow t\wedge (p\vee q)$
$p\vee q$
$\sim (p\vee (\sim p\wedge q\left)\right)=\sim (p\vee q)$
$=(\sim p)\wedge (\sim q)$