1. [This question shows a utility represents a preference relation if and only if it preserves strict preference and preserves indifference. This is a useful way to think about utility representation, and also gives you a different way of checking utility representation] Let f; be a preference relation on a set X , and let u : X > R. (a) Suppose u is a utility representation for z. Show that: i. Any :1; > y have u(;L) > u(y). ii. Any x N y have u(;z:) : u(y). (h) Suppose any a? > 3/ have \"(07) > Mg), and any a? N 3/ have \"(97) = \"(31). Show that In, is a utilitv representation for >