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Question 17 of 40

Q.If p∨qp \vee q is true, then the truth value of ∼p∧∼q\sim p \wedge \sim q is ______.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2022Subjective· 1mImportance★★★★★
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Using De Morgan's law, ∼p∧∼q≡∼(p∨q)\sim p \wedge \sim q \equiv \sim(p \vee q). Given p∨qp \vee q is true, ∼(p∨q)\sim(p \vee q) is false, so ∼p∧∼q\sim p \wedge \sim q is F.

By De Morgan's law of logic,

∼p∧∼q≡∼(p∨q).\sim p \wedge \sim q \equiv \sim(p \vee q).

We are told p∨qp \vee q is true (T). The negation of a true statement is false, so

∼(p∨q)≡F.\sim(p \vee q) \equiv \text{F}.

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