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  4. The negation of the Boolean expression ((∼ q ) ∧ p ) ⇒((∼ p ) ∨ q ) is logically equivalent to

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Q. The negation of the Boolean expression $((\sim q ) \wedge p ) \Rightarrow((\sim p ) \vee q )$ is logically equivalent to

JEE MainJEE Main 2022Mathematical Reasoning

Solution:

$\sim p \vee q \equiv p \rightarrow q$
$\sim q \wedge p \equiv \sim( p \rightarrow q )$
Negation of $\sim( p \rightarrow q ) \rightarrow( p \rightarrow q )$
is $\sim( p \rightarrow q ) \wedge(\sim( p \rightarrow q ))$ i.e. $\sim( p \rightarrow q )$