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JEE Main 20231 FebruaryMorning Shift

Exam: JEE Main
Year: 2023
Date: 1 February
Shift: Morning Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2023 · 1 February · Morning Shift · Mathematics · Mathematical Reasoning

The negation of the expression q ∨ ( ( ~ q ) ∧ p ) is equivalent to

The negation of the expression

q ∨ ( ( ~ q ) ∧ p )

is equivalent to

Options

A $( ~ p ) ∧ ( ~ q )$
B $p ∧ ( ~ q )$
C $( ~ p ) ∨ ( ~ q )$
D $( ~ p ) ∨ q$

Correct answer

A. $( ~ p ) ∧ ( ~ q )$

Step-by-step solution

The negation of $q ∨ ( ( ~ q ) ∧ p )$ is

$~ ( q ∨ ( ( ~ q ) ∧ p ) )$

$≡ ~ q ∧ ~ ( ( ~ q ) ∧ p )$

$≡ ~ q ∧ ( q ∨ ~ p )$

$≡ ( ~ q ∧ q ) ∨ ( ~ q ∧ ~ p )$

$≡ ( ~ q ∧ ~ p )$

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