Let A = {1,2,...,n}.

(a) How many relations are there on the set A?

(b) How many reflexive relations are there on the set A?

(c) How many symmetric relations are there on the set A?

(d) How many relations are there on the set A which are both reflexive and symmetric?

I think that the answer to (a) is $\displaystyle n^2$ because it will be ther number of ordered pairs, but this is just a guess.

If someone could point me in the right direction.