Q42 / 75 · JEE Main 2025 (22 Jan Shift 1) · Mathematics

The number of non-empty equivalence relations on the set $\{1,2,3\}$ is :

  • A
    $6$
  • Correct answer
    B
    $5$
  • C
    $7$
  • D
    $4$

Solution

Let $R$ be the required relation $\mathrm{A}=\{(1,1)(2,2),(3,3)\}$ (i) $|\mathrm{R}|=3$, when $\mathrm{R}=\mathrm{A}$ (ii) $|\mathrm{R}|=5$, e.g. $\mathrm{R}=\mathrm{A} \cup\{(1,2),(2,1)\}$ Number of $R$ can be [3] (iii) $\mathrm{R}=\{1,2,3\} \times\{1,2,3\}$ Ans. (5)

Hence, the correct answer is option: 'B'.

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