JEE Main 2022MathematicsMathematical ReasoningEasyMCQ

JEE Main 2022Mathematical Reasoning Question with Solution

JEE Main 2022 (26 Jun Shift 2)

Question

Let rP,q,~p,~q be such that the logical statement r~ppqr is a tautology. Then r is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C~p

Step-by-step explanation

Solving all option one by one we get following truth table,

(1)

p=r q ~p r~p pq pqr r~ppqr
T F F T F T T
F T T T F F F
T T F T T T T
F F T T F F T

(2)

p ~p r~p q=r pq pqr r~ppqr
T F T T T T T
F T T T F T T
T F F F F F T
F T T F F F F

(3)

p q r=~p r~p pq pqr r~ppqr
T T F F T T T
F T T T F T T
T F F F F F T
F F T T F T T

(4)

~p p q r~p r=~q pq pqr r~ppqr
F T T F F T T T
F T F T T F T T
T F T T F F F F
T F F T T F T T

Now final answer is option C.

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About this question

This is a previous-year question from JEE Main 2022, 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.