JEE Main 2022MathematicsMathematical ReasoningEasyMCQ

JEE Main 2022 — Mathematical Reasoning Question with Solution

JEE Main 2022 (27 Jul Shift 2)

Question

If the truth value of the statement P∧~R→~R∧Q is F, then the truth value of which of the following is F?

Choose an option

Show full solutionCorrect option: D
Correct answer
D~R∨Q→~P

Step-by-step explanation

We know that A→B is false, when A is true and B is false

So, for P∧~R→~R∧Q to be false, P∧~R should be true and ~R∧Q is false.

i.e P is true, R is false and Q is false.

A B A→B
T T T
T F F
F T T
F F T

Now, 

for P∨Q→~R is F→T≡T

R∨Q→~P is F→F≡T

~P∨Q→~R is T→T≡T

~R∨Q→~P is T→F≡F

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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.