JEE Main 2023MathematicsMathematical ReasoningEasyMCQ

JEE Main 2023 — Mathematical Reasoning Question with Solution

JEE Main 2023 (30 Jan Shift 1)

Question

Among the statements:

S1: p∨q⇒r⇔p⇒r

S2:p∨q⇒r⇔p⇒r∨q⇒r

Choose an option

Show full solutionCorrect option: B
Correct answer
BNeither (S1) nor (S2) is a tautology

Step-by-step explanation

We have,

S1: p∨q⇒r⇔p⇒r

For S1:  If p is F, q is T, r is F , then

p∨q⇒r≡F

p⇒r≡T

So, p∨q⇒r⇔p⇒r≡F

then F⇒F≡F

i.e. S1 is not a tautology

S2: p∨q⇒r⇔p⇒r∨q⇒r

S2:  If p is T, q is F, r is F , then

p∨q⇒r≡F

p⇒r∨q⇒r≡T

then p∨q⇒r⇔p⇒r∨q⇒r≡F

i.e. S2 is not a tautology

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About this question

This is a previous-year question from JEE Main 2023, covering the Mathematical Reasoning chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.