JEE Main 20205 SeptemberEvening Shift

Exam: JEE Main
Year: 2020
Date: 5 September
Shift: Evening Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2020 · 5 September · Evening Shift · Mathematics · Mathematical Reasoning

The statement (p → (q → p) ) → (p → (p ∨ q)) is :

The statement

\left(p \to \left(q \to p\right)

\right) \to \left(p \to \left(p ∨ q\right)\right) is :

Options

Aequivalent to $\left(p ∧ q\right) ∨ \left(~ q\right)
Ba contradiction
Cequivalent to $\left(p ∨ q\right) ∧ \left(~ p\right)
Da tautology

Correct answer

D. a tautology

Step-by-step solution

$p$	$q$	$q \to p$	$p ∨ q$	$r: p \to \left(q \to p\right)$	$s: p \to ( p ∨ q )$	$r \to s$
$T$	$T$	$T$	$T$	$T$	$T$	$T$
$T$	$F$	$T$	$T$	$T$	$T$	$T$
$F$	$T$	$F$	$T$	$T$	$T$	$T$
$F$	$F$	$T$	$F$	$T$	$T$	$T$

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