Question 2 [8 marks]. Recall that a set S Q IR" is convex if and only if, for any pair of points 131,32 E S and A E [Cl1 1], A31 + (1 )032 E S. (a) Let A, B f_: R\" be convex sets. Using the denition of convexity above (and no other properties of convex sets)1 prove that the intersection A r\": B is convex. (b) Consider the convex set S = {(m,y) : 3:2 + y2 g 1} (a unit circle). Find a non-convex set T g R2 such that 5' n T 15 and S n T is convex. In your answer, clearlyr explain why T is not convex and why the intersection S n T is convex