Let A = {a, b}. List all relation on A and find their number.
Any relation on A is a subset of A×A.
A×A = {(a, a), (a, b), (b, a), (b, b)}
The subsets are.
{} empty set
{(a, a)}
{(a, b)}
{(a, a), (a, b)}
{(b, a)}
{(b, b)}
{(b, a), (b, b)}
{(a, a), (b, a)}
{(a, b), (b, a)}
{(a, a), (b, a), (b, b)}
{(a, a), (b, b)}
{(a, a), (a, b), (b, a)}
{(a, a), (a, b), (b, b)}
{(a, b), (b, a), (b, b)}
{(a, a), (a, b), (b, a), (b, b)}
Thus, there are 16 total relations.