Question

Let $R$ be a reflexive relation on finite set $A$ having $n-$elements, and let there be $m-$ordered pairs in $R.$ Then

• A. $m\ge n$
• B. $m\le n$
• C. $m=n$
• D. Relation between $m\text{and}n$ cannot be determined.

Answer 1

The correct option is A $m\ge n$

Since $R$ is a reflexive relation on $A,$ therefore $(a,a)\in R$ for all $a\in A.$
So, the minimum number of ordered pairs in $R$ for it to be reflexive is $n.$
Hence, $m\ge n$