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Question: 1 40 points spencer says that he never finds himself...

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1. [40 points]. Spencer says that he never finds himself to be indifferent between two alternatives: he always strictly prefers one to the other. He also says that (1) if he had to choose from the set { A, C, D, F} he would choose D and (2) if he had to choose from the set A,B,D,E he would choose B; finally, (3) when asked whether he would rather choose from the set {A,C) or from the set C,F he said that he would strictly prefer choosing from the set C,F. Spencer is rational, in the sense that his preferences are complete and transitive (a) [8 points] How does Spencer rank Cversus F? Give a full and detailed explanation. (b) [8 points] How does Spencer rank A versus F? Give a full and detailed explanation (c) [14 points] For every pair (x,y) with x,ye{A, B,C D, E, F and x * y, state whether you can tell from the information above how Spencer ranks x versus y. (d) [10 points] Assuming that Spencer prefers E to D, write down all the complete and transitive relations that could represent Spencers preferences over the set (A,B. C,D. E.F)

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