Mathematics · Sets and Relations

JEE Main 2025 — 23 January, Morning Shift — Question 11

Let $\mathrm{R}=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$ . Then the minimum number of

elements, needed to be added in R so the R becomes an equivalence relation, is :

Answer: D

$A=\{1,2,3,4\}$

For relation to be reflexive

$\mathrm{R}=\{(1,2),(2,3),(3,3)\}$

Minimum elements added will be

$(1,1),(2,2),(4,4)(2,1)(3,2)(3,1)(1,3)$

$\therefore$ Minimum number of elements $=7$

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