Q. The logical statement $\left(p \Rightarrow q\right) ∧ \left(q \Rightarrow ~p\right)$ is equivalent to :

JEE MainJEE Main 2020Mathematical Reasoning Report Error

A

$\sim p$

B

$p$

C

$q$

D

$\sim q$

Solution:

$\left(p \to q\right) \wedge \left(q \to ~p\right)$
$\equiv \left(~p \vee q\right) \wedge \left(~q \vee ~p\right)$
$\equiv ~pv\left(q \wedge ~q\right)$
$\equiv ~p \vee C \equiv ~p$

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