Q2. 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: X > Y and Z > Y and Z ~ X Luis: X ~ Y and Z > Y and X > Z Lin: X Y and Z X (a) Do each person's preferences satisfy completeness? What about transi- 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 indifference curve for any of them? Explain