The maximum number of equivalence relations on the set A = {1, 2, 3} are

Answer

`5` such equivalence relations

Explanation

\begin{aligned}
&\mathrm{R}_{1}=\{(1,1),(2,2),(3,3)\} \\
&\mathrm{R}_{2}=\{(1,1),(2,2),(3,3),(1,2),(2,1)\} \\
&\mathrm{R}_{3}=\{(1,1),(2,2),(3,3),(1,3),(3,1)\} \\
&\mathrm{R}_{4}=\{(1,1),(2,2),(3,3),(2,3),(3,2)\} \\
&\mathrm{R}_{5}=\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)\} \\
\end{aligned}

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