JEE Main 2019 — Mathematical Reasoning Question with Solution
From: JEE Main 2019 (Online) 8th April Evening Slot
Question
Which one of the following statements is not a
tautology?
Choose an option
Show full solutionCorrect option: C
Correct answer
C( p q) ( p (~q))
Step-by-step explanation
Here you have to check all the options.
We know, p q = p q
(A) (p q) (~ p) q
= (p q) ((~ p) q)
= ( p q) ((~ p) q)
= p (q q)
= p t
[(q q) = t (tautology)]
= t
(B) (p q) p
= (p q) p
= p q p
= t q
= t
(C) ( p q) ( p (~q))
= ( p q) ( p (~q))
= ( p q) ( p (~q))
= q (p p)
= q t
= q (not tautology)
(D) p ( p q)
= p ( p q)
= t q
= t
We know, p q = p q
(A) (p q) (~ p) q
= (p q) ((~ p) q)
= ( p q) ((~ p) q)
= p (q q)
= p t
[(q q) = t (tautology)]
= t
(B) (p q) p
= (p q) p
= p q p
= t q
= t
(C) ( p q) ( p (~q))
= ( p q) ( p (~q))
= ( p q) ( p (~q))
= q (p p)
= q t
= q (not tautology)
(D) p ( p q)
= p ( p q)
= t q
= t
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