Can you provide the steps to solve this problem? I want to be able to check my steps so that I can get a better grasp on solving the problem.

Problem 5. (Difficult) You have read an article in a "prestigious" journal about a decision maker (DM) whose mental attitude toward elements in a finite set X is represented by a binary relation >, which is asymmetric and transitive but not necessarily complete. The incompleteness is the result of an assumption that a DM is sometimes unable to compare between alternatives. Another, presumably stronger, assumption made in the article is that the DM uses the following procedure: he has n criteria in mind, each represented by an ordering (asymmetric, transitive, and complete) >: (i = 1, ...,n). The DM decides that > > y if and only if r > y for every i. 1. Verify that the relation > generated by this procedure is asymmetric and transitive. Try to convince a reader of the paper that this is an attractive assumption by giving a "real life" example in which it is "reasonable" to assume that a DM uses such a procedure in order to compare between alternatives. It can be claimed that the additional assumption regarding the procedure that generates > is not a "serious" one since given any asymmetric and transitive relation, >, one can find a set of complete orderings >1, ...,>n such that x > y iff x >; y for every i. 2. Demonstrate this claim for the relation on the set X = {a, b, c} according to which only a > b and the comparison between [b and c] and [a and c] are not determined. 3. (Main part of the question) Prove this claim for the general case. Guid- ance (for c): given an asymmetric and transitive relation > on an arbi- trary X, define a set of complete orderings {} and prove that = > y iff for every i, > >. y