Prove (1) and (2) .
For (1), show that is an upper bound of .
For (2), use the fact that and imply .
I've found the following to be useful:
supremums of larger sets are larger and infimums of larger sets are smaller
Formally, (assuming the sets are bounded):
1. If then
2. If then
Proof of 1 - Let . Let , then and so ; i.e. is an upper bound of . So . The proof for infs is exactly similar.
For your original question, since , , and similarly for B.