Question

The negation of the statement $q\vee (p\wedge \sim r)$ is equivalent to

• A. $\sim q\wedge (p\to r)$
• B. $\sim q\wedge \sim (p\to r)$
• C. $\sim q\wedge (\sim p\wedge r)$
• D. None of these.

Answer 1

The correct option is A $\sim q\wedge (p\to r)$

The negation of the statement $q\vee (p\wedge \sim r)$ is
$\sim (q\vee (p\wedge \sim r\left)\right)\equiv \sim q\wedge (\sim p\vee \sim (\sim r\left)\right)\equiv \sim q\wedge (\sim p\vee r)\equiv \sim q\wedge (q\to r)$