Compound statement (∼( P wedge Q )) vee((∼ P ) wedge Q ) ⇒((∼ P ) wedge(∼ Q )) is equivale

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Mathematical Reasoning

hard

The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ is equivalent to

$((\sim P ) \vee Q ) \wedge((\sim Q ) \vee P )$

$(\sim Q) \vee P$

$((\sim P ) \vee Q ) \wedge(\sim Q )$

$(\sim P ) \vee Q$

(JEE MAIN-2023)

Solution

Let $\quad r =(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) ; \quad s =$ $((\sim P ) \wedge(\sim Q ))$

Option (A) : $((\sim P ) \vee Q ) \wedge((\sim Q ) \vee P )$ is equivalent to (not of only $P) \wedge($ not of only $Q$) $=($ Both $P , Q )$ and (neither $P$ nor $Q )$

Standard 11

Mathematics

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medium

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medium

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hard

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