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

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

JEE MainJEE Main 2023Mathematical Reasoning

Solution:

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