JEE Main 2021 — Mathematical Reasoning Question with Solution
From: JEE Main 2021 (Online) 22th July Evening Shift
Question
Which of the following Boolean expressions is not a tautology?
Choose an option
Show full solutionCorrect option: D
Correct answer
D( p q) ( q p)
Step-by-step explanation
(1) (p q) ( q p)
= ( p q) (q p)
= ( p p) q
= t q = t
(2) (q p) ( q p)
= ( q p) (q p)
= ( q q) p
= t p = t
(3) (p q) ( q p)
= ( p p) (q p)
= ( p p) ( q q)
= t t = t
(4) ( q q) ( q p)
= (p q) (q p)
= (p p) (q p)
= p q
Which is not a tautology.
= ( p q) (q p)
= ( p p) q
= t q = t
(2) (q p) ( q p)
= ( q p) (q p)
= ( q q) p
= t p = t
(3) (p q) ( q p)
= ( p p) (q p)
= ( p p) ( q q)
= t t = t
(4) ( q q) ( q p)
= (p q) (q p)
= (p p) (q p)
= p q
Which is not a tautology.
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