Economics question

2. For the proof of the second welfare theorem, we introduced the concept of the (Minkowski) sum of sets in Euclidean space, A + B = {a + b | a belongs to A and b belongs to B}. We also claimed without proof in lecture that A + B is a convex set if both A and B are convex. [35 points total] (a) Define convexity of S, where S is a subset of Euclidean space. [5 points] (b) Prove that A + B is convex whenever A and B are convex sets. [15 points] (c) Discuss where this is used in the proof and explain its role in the proof. [Note: Do not attempt to give a complete proof of the second welfare theorem in your answer.] [15 points]