Hi, I need help with my game theory assignment. Thank you.

(10 points (bonus)) (*) Suppose that you know X is nite, and t is a rational pref erence relation on X. Follow the following steps to show how to construct a utility function. 0 First, that there must be a (non-strictly) a worst element in X (i.e. Elm E X such that V56 6 X,:c : m) 0 Similarly, argue there must be a best element in X. 0 Next, argue that for each element there is a number 29,, which represent the number ofy E X such that a: t y. 0 Use this to construct a utility function. 0 Finally, argue that if u(a:) 2 u(a:) then :1: t y