A definition in my Abstract Algebra class on an ordered pair is as follows:

Let A and B be sets. Given a is an element of A and b is an element of B, the ordered pair (a,b) is the set {{a},{a,b}}.

Why isn't it {{a}, {a,b}, {b}} ? Or just {a,b}?

I guess I don't understand why {a} is included.

Any help would be greatly appreciated.