Let us suppose that A is a set having n elements.

A relation on a set A is a collection of ordered pairs of elements of A.

So the total number of possible order pairs = n²

Now for a given relation R, every element of A² may be either present or not.

So total number of possible relations = 2ⁿ

Again for a relation to be reflexive, all the ordered pairs (i, i) where i = 1, 2, 3,.........,n must be present

The remaining (n² - n) ordered pairs either present or not.

So it gives total 2ⁿ² - n possible relations.

Hense total reflexive relation is 2ⁿ² - n