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JEE Main 202227 JuneEvening Shift

Exam: JEE Main
Year: 2022
Date: 27 June
Shift: Evening Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2022 · 27 June · Evening Shift · Mathematics · Mathematical Reasoning

Which of the following statement is a tautology?

Which of the following statement is a tautology?

Options

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

Correct answer

C. $\left(\left(~ q\right) ∧ p\right) ∨ \left(p ∨ \left(~ p\right)\right)$

Step-by-step solution

We know that $p ∨ ~ p$ is a tautology and $r ∨ t ≡ t$

So,\left( $\left(~ q\right)$ ∧ p\right) ∨ \left(p ∨ $\left(~ p\right)\right)$ will be a tautology.

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