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  4. Let p and q be two statements. Then ∼(p ∧(p ⇒ ∼ q)) is equivalent to

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Q. Let $p$ and $q$ be two statements. Then $\sim(p \wedge(p \Rightarrow \sim q))$ is equivalent to

JEE MainJEE Main 2023Mathematical Reasoning

Solution:

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