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JEE Main 202116 MarchMorning Shift

Exam: JEE Main
Year: 2021
Date: 16 March
Shift: Morning Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2021 · 16 March · Morning Shift · Mathematics · Mathematical Reasoning

Which of the following Boolean expression is a tautology ?

Which of the following Boolean expression is a tautology ?

Options

A $\left(p ∧ q\right) ∨ \left(p ∨ q\right)$
B $\left(p ∧ q\right) ∨ \left(p \to q\right)$
C $\left(p ∧ q\right) ∧ \left(p \to q\right)$
D $\left(p ∧ q\right) \to \left(p \to q\right)$

Correct answer

D. $\left(p ∧ q\right) \to \left(p \to q\right)$

Step-by-step solution

$p$	$q$	$p ∧ q$	$p \to q$	\left(p ∧ q\right) \to \left(p \to q\right)
$T$	$T$	$T$	$T$	$T$
$T$	$F$	$F$	$F$	$T$
$F$	$T$	$F$	$T$	$T$
$F$	$F$	$F$	$T$	$T$

$\left(p ∧ q\right)$ \to \left(p \to q\right) is tautology

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