JEE Main 2023MathematicsMathematical ReasoningEasyMCQ

JEE Main 2023 — Mathematical Reasoning Question with Solution

JEE Main 2023 (01 Feb Shift 2)

Question

Which of the following statements is a tautology?

Choose an option

Show full solutionCorrect option: B
Correct answer
Bp∧q→~p→q

Step-by-step explanation

We know,

A→B≡~A∨B

Now solving all options one by one we get,

A p→p∧p→q

≡~p∨p∧~p∨q

≡~p∨f∨p∧q

≡~p ∨p∧q≡~p∨p∧~p∨q

≡~p ∨ q

Which is not a tautology

B p∧q→~p→q

≡~p∧q∨p∨q

≡~p∨~q∨p∨q

≡~p∨p∨~q∨q

≡T∨T≡T

Tautology

C p∧p→q→~q

≡~p∧~p∨q∨~q

≡~p∧q∨~q

≡~p∨~q

Which is not a tautology

D p∨p∧q≡p

Which 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.