Let p, q, r be three logical statements. Consider the compound statements S _ 1 : ( (~ p) ∨ q) ∨ ((~ p) ∨ r) and S _ 2 : p → (q ∨ r) Then, which of the following is NOT true?

Correct answer: C. If S _ 2 is False, then S _ 1 is True S _ 1 : (~ p ∨ q) ∨ (~ p ∨ r) ≡ ~ p ∨ (q ∨ r) S _ 2 : p → (q ∨ r) ≡ ~ p ∨ (q ∨ r) So S _ 1 is equivalent to S _ 2

JEE Main 202228 JuneMorning Shift

Exam: JEE Main
Year: 2022
Date: 28 June
Shift: Morning Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2022 · 28 June · Morning Shift · Mathematics · Mathematical Reasoning

Let p, q, r be three logical statements. Consider the compound...

Let $p, q, r$ be three logical statements. Consider the compound statements
${S}_{1}:$ \left( $\left(~ p\right) ∨ q\right) ∨ \left(\left(~ p\right) ∨ r\right)$ and ${S}_{2}: p \to \left(q ∨ r\right)$
Then, which of the following is NOT true?

Options

AIf ${S}_{2}$ is True, then ${S}_{1}$ is True
BIf ${S}_{2}$ is False, then ${S}_{1}$ is False
CIf ${S}_{2}$ is False, then ${S}_{1}$ is True
DIf ${S}_{1}$ is False, then ${S}_{2}$ is False

Correct answer

C. If ${S}_{2}$ is False, then ${S}_{1}$ is True

Step-by-step solution

{S}_{1}: \left(~ p ∨ q\right) ∨ \left(~ p ∨ r\right) $</p><p>$ ≡ ~ p ∨ \left(q ∨ r\right) $</p><p>$ {S}_{2}: p \to \left(q ∨ r\right) $≡ ~ p ∨ \left(q ∨ r\right)$

So ${S}_{1}$ is equivalent to ${S}_{2}$

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