JEE Main 2023MathematicsMathematical ReasoningEasyMCQ

JEE Main 2023 — Mathematical Reasoning Question with Solution

JEE Main 2023 (13 Apr Shift 2)

Question

The statement (p∧(~q))∨((~p) ∧ q) ∨((~p) ∧ (~q)) is equivalent to _____

Choose an option

Show full solutionCorrect option: B
Correct answer
B~p∨~q

Step-by-step explanation

Given,

(p∧(~q))∨((~p) ∧ q) ∨((~p) ∧ (~q))

=((~p) ∧ q) ∨((~p) ∧ (~q))∨(p∧(~q))

=~p∧q∨~q∨p∧~q

We know that ~A∨A=T, where T is tautology,

=~p∧T∨p∧~q

=~p∨p∧~q

=~p∨p∧~p∨~q

=T∧~p∨~q

=~p∨~q

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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.