I'm having problems with some of the proofs of the supremum and infimum properties in my text. here are two that I'm stuck on:

a) Let S be a non-empty subset ofRthat is bounded below. Prove that

inf S = -sup{-s: s in S}

b) Let A and B be bounded non-empty subsets ofR, and let

A+B := {a+b: a in A, b in B}.

Prove that sup(A+B) = supA + supB and inf(A+B) = infA + infB

Any comments and/or help would be much appreciated, it's getting near the end of the semester, and I'm really struggling with these concepts!

-Robitar