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Implication

Negation of t...

Question

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

A

\sim p \to\sim (q \lor r)

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B

\sim p \to\sim (q \land r)

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C

(q \lor r) \to p

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D

p \land (\sim q \land \sim r)

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Solution

The correct option is D $p \land (\sim q \land \sim r)$
We know that, $\sim (p \to q) \equiv p \land (\sim q)$
Also, negation of $(q \lor r)$ is $(\sim q \land \sim r)$
So, $\sim (p \to (q \lor r)) \equiv p \land (\sim q \land \sim r)$

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