JEE Main 2022 — Mathematical Reasoning Question with Solution
From: JEE Main 2022 (Online) 26th June Morning Shift
Question
Let , {, } be such that p q ((p q) r) is a tautology. Then (p q) r is logically equivalent to :
Choose an option
Show full solutionCorrect option: A
Correct answer
A(p r) q
Step-by-step explanation
Case-I
If is same as
Then
is equivalent to
is equivalent to
Which cannot be a tautology
For both (i.e. or )
Case-II
If is same as
Then is equivalent to
which can be a tautology if is also same as .
Hence both and are same as .
Now is equivalent to .
If is same as
Then
is equivalent to
is equivalent to
Which cannot be a tautology
For both (i.e. or )
Case-II
If is same as
Then is equivalent to
which can be a tautology if is also same as .
Hence both and are same as .
Now is equivalent to .
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Mathematical Reasoning chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →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.