Question

Let $\mathrm{R}$ be an equivalence relation on a finite set $\mathrm{A}$ having $\mathrm{n}$ elements. Then the number of ordered pairs in $\mathrm{R}$ is

• A. $>n$
• B. $\le n$
• C. $\ge n$
• D. None of the above

Answer 1

The correct option is B

$\le n$

Explanation for the correct option:

Since $\mathrm{R}$ is an equivalence relation on set $A$,$(\mathrm{a},\mathrm{a})\in \mathrm{R}$ for all$a\in A$.

Hence,$\mathrm{R}$ has at least $\mathrm{n}$ ordered pairs.

Hence, the correct answer is Option (B).