JEE Main 2023MathematicsMathematical ReasoningEasyMCQ

JEE Main 2023 — Mathematical Reasoning Question with Solution

JEE Main 2023 (25 Jan Shift 1)

Question

The statement p∧~q⇒p⇒~q is

Choose an option

Show full solutionCorrect option: B
Correct answer
Ba tautology

Step-by-step explanation

Using logical equivalence condition p→q≡~p∨q, given statement can be expressed as, 

p∧~q→p→~q

≡ ~p∧~q∨~p∨~q.......(1)

We know De Morgan's law of logical equivalence is,

~p∧q≡~p∨~q

Applying De Morgan's law in equation(1) we get,

≡ ~p∨q∨~p∨~q   ∵~~p≡p

≡ ~p∨~p∨q∨~q

≡~p∨t≡t (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.