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

Question

Aicharya · Accepted Answer

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) .

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

Solution