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JEE Main 202125 JulyMorning Shift

Exam: JEE Main
Year: 2021
Date: 25 July
Shift: Morning Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2021 · 25 July · Morning Shift · Mathematics · Mathematical Reasoning

The Boolean expression ( p ⇒ q ) ∧ ( q ⇒ ~ p ) is equivalent to :

The Boolean expression

( p ⇒ q ) ∧ ( q ⇒ ~ p )

is equivalent to :

Options

A $~ q$
B $q$
C $p$
D $~ p$

Correct answer

D. $~ p$

Step-by-step solution

$( p ⇒ q ) ∧ ( q ⇒ ~ p )$

$= ( ~ p ∨ q ) ∧ ( ~ q ∨ ~ p )$ ${ p ⇒ q = ~ p ∨ q }$

$= ( ~ p ∨ q ) ∧ ( ~ p ∨ ~ q )$ {commutative property}

$= ~ p ∨ ( q ∧ ~ q )$ {distributive property}

$= ~ p$

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