JEE Main 2023MathematicsSets and RelationsMediumNumerical

JEE Main 2023 — Sets and Relations Question with Solution

JEE Main 2023 (24 Jan Shift 2)

Question

The minimum number of elements that must be added to relation R=a,b,b,c,b,d on the set a,b,c,d, so that it is an equivalence relation is

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Show full solutionCorrect answer: 13
Correct answer
13

Step-by-step explanation

Let

A={a, b, c,d}, R : A→A

R=a,b,b,c,b,d

Reflexive:

For reflexivity, we must add a,a, b,b, c,c, d,d

Symmetric and Transitive:

For symmetric and transitivity, we must add

b,a, c,b, d,b

a,c, a,d, c,d, d,c, c,a, d,a

So, we can say that minimum 13 elements are required to make an equivalence relation.

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About this question

This is a previous-year question from JEE Main 2023, 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.