Question

Let $R$ be an equivalance relation on a finite set $A$ having $n$ elements. Then, the number of ordered pairs in $R$ is

• A. less than $n$
• B. greater than or equal to $n$
• C. less than or equal to $n$
• D. None of these

Answer 1

The correct option is B greater than or equal to $n$

Let $A=\{a_1,a_2,a_3,\dots ,a_n\}$
There are $n$ elements in $A$.
Since, the relation is reflexive, the number of ordered pairs must be greater than or equal to $n$, as $\forall a\in A\Rightarrow (a,a)\in R$