Q52 / 90 · JEE Main 2019 (12 Apr Shift 2) · Mathematics

The Boolean expression $\sim (p \Rightarrow (\sim q))$ is equivalent to

A
$(\sim p) \Rightarrow q$
B
$q \Rightarrow \sim p$
C
$p \lor q$
Correct answer
D
$p \land q$

Solution

Recall $p \Rightarrow q \equiv ~ p \lor q$

$\sim (p \Rightarrow (\sim q)) = \sim (\sim p \lor \sim q)$
$= p \land q$

Hence, the correct answer is option: 'D'.

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