For each of the following statements, either prove that it is true, or give a counterexample showing that it is false in general. a. If G and C are convex, then CUC, is convex. b. If C and Care (not necessarily convex) cones, then CUC is a (not necessarily convex) cone. c. Consider the set of points x defined by finitely many linear inequalities, i.e., the set of points x defined by Ax