Question

The negation of $p\land \left(q \rightarrow \sim r\right)$ is?

• A. $\sim p\land \left(q \land r\right)$
• B. $p\lor \left(q \lor r\right)$
• C. $p\lor \left(q \land r\right)$
• D. $\sim p\lor \left(q \land r\right)$

Answer 1

Answer: (D)

Let, $X=\sim p \wedge q \rightarrow \sim r$
We know that
$\sim p \wedge q=\sim p \vee \sim q \text { and } \sim p \rightarrow q=p \wedge \sim q $
$\therefore X=\sim p \vee \sim q \rightarrow \sim r$
$X=\sim p \vee q \wedge \sim \sim r $
$X=\sim p \vee q \wedge r$