4. [12 Marks] Assume that the set of alternatives is X = R. and consider the preference relation > such that, for any r, y ( X, a > y if and only if =1 2 11 or 12 2 1/2. (a) (2 marks) Illustrate the indifference curves of this preference relation. (b) (2 marks) Is this preference relation complete? Provide an explanation. (c) (2 marks) Is this preference relation transitive? Provide an explanation. (d) (2 marks) Is this preference relation monotone? Provide an explanation. (e) (2 marks) Is this preference relation convex? Use a diagram to provide an explana tion. (f) (2 marks) Provide a utility function w(21, 12) that represents this preference relation if possible. If not possible, explain why not