Logical statement (p ⇒ q){wedge}(q ⇒ ∼ p) is equivalent to

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Mathematical Reasoning

hard

The logical statement $(p \Rightarrow q){\wedge}(q \Rightarrow \sim p)$ is equivalent to

A

$p$

B

$q$

C

$\sim p$

D

$\sim q$

(JEE MAIN-2020)

Solution

$(p \rightarrow q) \wedge(q \rightarrow \sim p)$

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

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

$\equiv \sim p \vee C \equiv \sim p$

Standard 11

Mathematics

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