JEE Main 2021MathematicsSets and RelationsMediumMCQ

JEE Main 2021 — Sets and Relations Question with Solution

JEE Main 2021 (31 Aug Shift 1)

Question

Which of the following is not correct for relation R on the set of real numbers?

Choose an option

Show full solutionCorrect option: D
Correct answer
D(x,y)∈R⇔0<|x|-|y|≤1 is not transitive but symmetric.

Step-by-step explanation

We know that (x, y)∈R , (y, x)∈R ⇒symmetric

(x, y)∈R , (y, z)∈R & (z, x)∈R⇒transitive
0<|x-y|≤10<|y-x|≤1is symmetric

let 

0<|x-y|≤1                                         .......(1)
(1,2)∈R and (2,3)∈R satisfy the equation (1)
but (1,3)∉R not satisfied
Hence 0<|x-y|≤1 is symmetric but not transitive relation

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About this question

This is a previous-year question from JEE Main 2021, covering the Sets and Relations 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.