2. Answer all parts (a) - (g) of this question. James can afford to buy one of three cars: the Aleph, the Beth or the Gimel. He rates them on three criteria. On looks he rates the Aleph best, the Beth second best and the Gimel the worst. On road handling he rates the Beth the best, the Gimel second best and the Aleph worst. Finally, on safety he rates the Gimel the best, the Aleph second best and the Beth worst. He decides that he weakly prefers one car (say A) to another (say B) if and only if he prefers A to B on at least as many of these three criteria as he prefers B to A. He strongly prefers A to B if he weakly prefers A to B and doesn't weakly prefer B to A. Are the following statements true or false? Briefly justify your answers. (a) [3 marks] James strongly prefers Aleph to Beth. (b) [3 marks] James weakly prefers Gimel to Beth. (c) [3 marks] James weakly prefers Gimel to Aleph. (d) [4 marks] James' preference relation satisfies completeness. (e) [4 marks] James' preference relation satistfies transitivity. (f) [4 marks] James' preference relation satisfies reflexivity. (g) [4 marks] James should be considered indifferent between the three cars