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Logical Connectives

Negation of t...

Question

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

A

\sim p \to (q \lor r)

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B

p \lor (q \land r)

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C

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

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D

p \land (q \lor r)

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Solution

The correct option is A $\sim p \land (\sim q \land \sim r)$
We know that $\sim (p \to q) ≅ p \land \sim q$
So, we have, $\sim (\sim p \to (q \lor r)) \equiv\sim p \land \sim (q \lor r)$
$\equiv\sim p \land (\sim q \land \sim r)$

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