6. (20 points) Let X = R2. Let ~ be a preference relation on X. In Lecture notes-2 (see Lecture 2, page 7, Definition 9) we have encountered the definition of additivety property of a preference relation. (a) (10 points) Suppose that the preference relation ~ is represented by the utility function u(1, X2) where, u(1, 12) = Qx1 + 3x2 where a, B > 0. Verify that the preference relation ~ satisfies addivity and strict monotonicity. 2