Let A = {a, b}. List all relation on A and find their number.

Question

Philoid · Accepted Answer

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.