Given a set S, a function f: S X S S is called a binary operation on S. If S is a finite set, then how many different binary operations on S are possible?
I have no clue on this one? Could someone point me in the right direction?
I realize that if S has n elements then SxS would have possible ordered pairs. However, I'm not sure what is meant by how many different binary operations. Would we have addition, subtraction, multiplication, division, exponentiation, etc. times binary operations?