I'm having some difficulty with these two problems,any help is appreciated.

1)Prove that given is not empty

Since B is not empty, let , then it follows , so LHS= such that . This doesn't look right, so anyone can help me figure out what I did wrong here.

2) Is it true that ? When does equality hold?

Here, can I take the empty set to be B, and the equality will be false because the empty set doesn't contain any element, but we need . Is my argument correct? I can't find condition such that equality holds.