Jane chooses alternatives indexed by integers ranging from 10 to 10: 10, 9, ..., 1, 0, 1, ..., 10. She is presented with sets of three distinct alternatives. For each description of Jane's choice function for each such set, explain whether Jane has rational preferences or not. If she does, explicitly show a utility function for Jane that rationalises her choices.

a) For each set of three alternatives, Jane chooses the alternative(s) that are the closest to 0 (e.g., in set {3, 2, 2} Jane would pick alternatives 2 and 2).