Let $R$ be an equivalence relation defined on a set containing 6 elements. The minimum number or ordered pairs that $R$ should contain is

Given that, $\mathrm{R} \rightarrow$ equivalence relation on a set $\mathrm{A}$ Let $\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\}$ Since, $R$ is an equivalence relation on set $A$, then it must be satisfies reflexive property, for this. $$ \mathrm{aRa}, \forall \mathrm{a} \in \mathrm{A} $$ That mean minimum number of elements in ' $R$ ' should be six $e g, \quad \mathrm{R}=\{(\mathrm{a}, \mathrm{a}),(\mathrm{b}, \mathrm{b}),(\mathrm{c}, \mathrm{c}),(\mathrm{d}, \mathrm{d})$ $(e, e),(f, f)\}$