JEE MAIN - Mathematics (2025 - 23rd January Morning Shift - No. 20)
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 that R becomes an equivalence relation, is:
9
8
7
10
Explanation
$$\mathrm{A}=\{1,2,3,4\}$$
For relation to be reflexive
$$\mathrm{R}=\{(1,2),(2,3),(3,3)\}$$
Minimum elements added will be
$$\begin{aligned} & (1,1),(2,2),(4,4)(2,1)(3,2)(3,2)(3,1)(1,3) \\ & \therefore \text { Minimum number of elements }=7 \end{aligned}$$
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