Question

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

Answer 1

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.