Question

The negation of the compound statement $p\vee (\sim p\vee q)$ is ___.

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

Answer 1

The correct option is A

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

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