Originally Posted by

**oldguynewstudent** Given a set S, a function f: S X S $\displaystyle \longrightarrow$ 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 $\displaystyle n^2$ 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 $\displaystyle n^2$ binary operations?