2. [The previous question gave you a different way of checking utility representa- tion. This question gives you practice applying it.] Consider the set X = {Jerry, George, Elaine, Cosmo}. (a) Explain why there is exactly one preference relation _ on X that has Elaine > George, George ~ Cosmo, and Cosmo > Jerry. [Note, you need to explain both why some such preference relation exists and why there cannot be two different such preference relations.] This is the "is funnier than" relation. (b) Let ~ be the preference relation from part (a). Define the function u : X - R given by u (x) Jerry 0 Elaine 42 George 10 Cosmo 10 i. Explain why any x, y E X with x > y have u(x) > u(y). [Hint: You need to worry about every x, y E X with x > y. In particular, Elaine > George and Cosmo > Jerry are not the only two such pairs you need to worry about.] ii. Explain why any x, y E X with x ~ y have u(x) = u(y)