Given the following two statements: ( S _ 1 ): (q ∨ p) → (p ↔ ~ q) is a tautology ( S _ 2 ) : ~ q ∧ (~ p ↔ q) is a fallacy. Then :

Correct answer: A. both ( S _ 1 ) and ( S _ 2 ) are not correct. p q ~ p ~ q q ∨ p p ↔ ~ q S _ 1 : (q ∨ p) → (p ↔ ~ q) ~ p ↔ q S _ 2 : ~ q ∧ (~ p ↔ q) T T F F T F F F F T F F T T T T T T F T T F T T T T F F F T T F F T F F So both ( S _ 1 ) and ( S _ 2 ) are not correct.

JEE Main 20204 SeptemberMorning Shift

Exam: JEE Main
Year: 2020
Date: 4 September
Shift: Morning Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2020 · 4 September · Morning Shift · Mathematics · Mathematical Reasoning

Given the following two statements: ( S _ 1 ): (q ∨ p) → (p ↔ ~ q)...

Given the following two statements:

$\left({S}_{1}\right): \left(q ∨ p\right)$ \to \left(p ↔ ~ q\right) $is a tautology<br />\left({S}_{2}\right)$ : ~ q ∧ \left(~ p ↔ q\right) is a fallacy. Then :

Options

Aboth $\left({S}_{1}\right)$ and $\left({S}_{2}\right)$ are not correct.
Bonly $\left({S}_{1}\right)$ is correct.
Conly $\left({S}_{2}\right)$ is correct.
Dboth $\left({S}_{1}\right)$ and $\left({S}_{2}\right)$ are correct.

Correct answer

A. both $\left({S}_{1}\right)$ and $\left({S}_{2}\right)$ are not correct.

Step-by-step solution

$p$	$q$	$~ p$	$~ q$	$q ∨ p$	$p ↔ ~ q$	${S}_{1}: \left(q ∨ p\right)$ \to \left(p ↔ ~ q\right) $</td> <td style="text-align: center;">$ ~ p ↔ q $</td> <td style="text-align: center;">$ {S}_{2}: ~ q ∧ \left(~ p ↔ q\right)
$T$	$T$	$F$	$F$	$T$	$F$	$F$	$F$	$F$
$T$	$F$	$F$	$T$	$T$	$T$	$T$	$T$	$T$
$F$	$T$	$T$	$F$	$T$	$T$	$T$	$T$	$F$
$F$	$F$	$T$	$T$	$F$	$F$	$T$	$F$	$F$

So both \left({S}_{1}\right) $and \left({S}_{2}\right) are not correct.$

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