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

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

JEE MainJEE Main 2020Mathematical Reasoning

Solution:

Negation of $\phi \vee(\sim p \wedge q)$
$p \vee(\sim p \wedge q )=( p \vee \sim p ) \wedge( p \vee q )$
$=( T ) \wedge( p \vee q )$
$=( p \vee q )$
now negation of $( p \vee q )$ is
$\sim( p \vee q )=\sim p \wedge \sim q$