Hi! I am studying for my finals and I need some help. Thank you so much in advance.

1) Prove that the set F(S) of finite subsets of a countable set S is countable, and it is (countably) infinite if and only if S is (countably) infinite.

2) Suppose that E is an equivalence relation on a countably infinite set S, and let S/E be the associated family of eqivalence classes. Explain why S/E is countable.