Take X and E; where t is a complete and transitive binary relation on X. For a given a E X, dene HI} = {y .' y w 1:} Le, Hm] is the collection of all alternativm that yield the same satisfaction as :c. Prove that the set (of sets) {Hm} : z E X} is a partition of X. That is, two conditions hold. [a] For each 3E I there is y E Xsnch m E Hy}. (h) For each say E X, either Hm) = y} or Hm} y} = ill