QJEEM23Ma0cd4: JEE Main 2023 Mathematics - Class 11 JEEM23Ma0cd4 Solution: The negation of the statement ( p ∨ q ) ∧ ( q ∨ ( ∼ r ) ) is :

Question

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The negation of the statement $(p \lor q) \land (q \lor (\sim r))$ is :

Accepted Answer

The negation of the statement

(p \vee q) \wedge(q \vee(\sim r))

is

\begin{aligned} =\sim [(p \lor q) \land (q \lor (\sim r))] \\ =\sim [(p \lor q) \lor \sim (q \lor (\sim r)] \\ = ((\sim p) \land \sim q)) \lor ((\sim q) \land r)) \end{aligned}

Apply distribution law,

\begin{aligned} =\sim q \land ((\sim p) \lor r)) \\ = ((\sim p) \lor r) \land (\sim q) \end{aligned}

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