5. (20 points) The purpose of this problem is to make sure that you fully understand the basic concepts of utility representation Prove or disprove the following statements. (a) (10 points) Is the statement "a continuous preference relation have a utility func- tion representation that is discontinuous" correct ? (b) (10 points) Is the statement "If both u and v are utility functions representing the preference relation ~ then there is a strictly monotonic function f : R - R (i.e., f is strictly increasing) such that v = f(u)," correct