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BITSAT 2018

Exam: BITSAT
Year: 2018
Subject: Mathematics
Chapter: Mathematical Reasoning

BITSAT 2018 · Mathematics · Mathematical Reasoning

Which of the following statement is a tautology?

Which of the following statement is a tautology?

Options

A $\left(p ∨ q\right) ∨ \left( p\right)$
B $\left( q ∧ p\right) ∨ \left(p ∨ p\right)$
CBoth (a) and (b)
DNone of the above

Correct answer

C. Both (a) and (b)

Step-by-step solution

Truth table

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

Hence, option (c) is correct.

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