Question

Negation of the statement $p\wedge (q\wedge r)$ is equivalent to

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

Answer 1

The correct option is D $\sim p\vee (\sim q\vee \sim r)$

We have to find negation of $p\wedge (q\wedge r)$

$=\sim (p\wedge (q\wedge r))=\sim p\vee \sim (q\wedge r)[\sim (A\wedge B)\equiv \sim A\vee \sim B]=\sim p\vee (\sim q\vee \sim r)$