For example, if the Dog Pound held the dogs Fido, Rex and Spot, then A x A would be:
{ (Fido, Fido), (Fido, Rex), (Fido, Spot), (Rex, Fido), (Rex, Rex), (Rex, Spot), (Spot, Fido), (Spot, Rex), (Spot, Spot) }
One relation on A could be that for any x, y in A, x~y if their names are the same length.
You can define any relation on A in terms of a subset of A x A.
In this case, it would be:
{ (Fido, Fido), (Fido, Spot), (Rex, Rex), (Spot, Fido), (Spot, Spot) }
]]>1) Describe A x A
2) Give an example of a relation on A.