Prove Inductively: Discrete Math 2

Problem 2. Let A be a set and R, S are two equivalence relations on A. Prove the following: (a) RnS is an equivalence relation on A (b) RUS may not be an equivalence relation on A. Give a counterexample to show how this fails. (c) Now consider A = Z and consider the two equivalence relations What is the relation Rn S? (d) If R has n equivalence classes and S has m equivalence classes, how many equivalence classes does RnS have