5. Let A be a set and let be a binary operation on A. We say that a subset B A is closed under if for all a1, a2 B, a1a2 B. (a) Prove that, if subsets B and C of A are closed under , then the intersection, B C, is also closed under . (b) For a Z, define the set aZ = {ak : k Z}. Prove that aZ is closed under the addition operation on Z. (You can take for granted the usual arithmetic properties of Z.)