(5) A subset M of the plane is called a convex set if for every two points P and Q in M the segment PQ is entirely contained in M. (a) Prove that the intersection of two convex sets is a convex set. (b) Prove that a segment AB is a convex set. (c) Prove that a half-plane is a convex set. (d) Is the interior of an angle a convex set? What about the exterior of an angle?