Imagine that there are three choices for lunch on the menu: X = sandwich, Y = sushi and Z = salad. Tanmay. Luis and Lin have the following preferences regarding lunch: Tanmay: XZY andZzY andZzX Luis: X~Y andZzY andXZZ Lin: X>Y andZ>X (a) Do each person's preferences satisfy completeness? What about transi- 1 tivity? Explain. (b) What additional preference relationship would you add to the list for Lin to ensure that her preferences are rational? Explain. (c) Would X and Y lie on the same indierence curve for any of them? Explain.