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  4. The proposition p arrow ∼( p ∧ ∼ q ) is equivalent to:

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Q. The proposition $p \rightarrow \sim( p \wedge \sim q )$ is equivalent to:

JEE MainJEE Main 2020Mathematical Reasoning

Solution:

$p \rightarrow \sim( p \wedge \sim q )$
$=\sim p \vee \sim( p \wedge \sim q )$
$=\sim p \vee \sim p \vee q$
$=\sim( p \wedge q ) \vee q$
$=\sim p \vee q$