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  4. The Boolean expression ∼ ( p ∨ q) ∨ (∼ p ∧ q) is equivalent to :

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

JEE MainJEE Main 2018Mathematical Reasoning

Solution:

$\sim(p \vee q) \vee(\sim p \wedge q)$
By property, $(\sim p \wedge \sim q) \vee(\sim p \wedge q)$
$=\sim p$