Hi! I really need help on this one problem:

Suppose that R1 and R2 are equivalence relations on the set S. Determine whether each of these combinations of R1 and R2 must be an equivalence relation.

a) R1 U R2

b) R1 ^ R2 (^ = intersection)

Please respond ASAP. This assignment is due tomorrow morning. I'm really sorry for making it so last minute. Thank you so much for being super awesome!

Edit: I guess I should add that I think a) is not an equivalence relation and b) is a equivalence relation though I don't know how to prove it.