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  4. The statement (p ∧(∼ q)) ⇒(p ⇒(∼ q)) is

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Q. The statement $(p \wedge(\sim q)) \Rightarrow(p \Rightarrow(\sim q))$ is

JEE MainJEE Main 2023Mathematical Reasoning

Solution:

$( p \wedge \sim q ) \rightarrow( p \rightarrow \sim q ) $
$ \equiv(\sim( p \wedge \sim q )) \vee(\sim p \vee \sim q ) $
$ \equiv(\sim p \vee q ) \vee(\sim p \vee \sim q )$
$ \equiv \sim p \vee t \equiv t $