JEE Main 2023MathematicsMathematical ReasoningEasyMCQ

JEE Main 2023 — Mathematical Reasoning Question with Solution

JEE Main 2023 (12 Apr Shift 1)

Question

Among the two statements

S1:p⇒q∧p∧~q is a contradiction and S2:p∧q∨~p∧q∨p∧~q∨~p∧~q is a tautology

Choose an option

Show full solutionCorrect option: D
Correct answer
Dboth are true

Step-by-step explanation

Given,

S1:p⇒q∧p∧~q

≡~p∨q∧p∧~q as A⇒B≡~A∨B

≡~p∧p∧~q∨q∧p∧~q

≡f∧~q∨f∧p

≡f∨f≡f

 

S2:p∧q∨~p∧q∨p∧~q∨~p∧~q

≡p∧q∨~p∧q∨p∧~q∨~p∧~q

≡p∨~p∧q∨p∨~p∧~q

≡t∧q∨t∧~q≡q∨~q≡t

Hence, both statement are true.

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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.