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Midterm PHIL 339 Due 4:50pm on T 11/2 Answer five of the following seven questions. You are welcome to use the book and handouts, but no other resources. Collaboration is prohibited. Please upload to Blackboard or leave in my mailbox in MHP 113. Late work will not be accepted. 1. Suppose that R is a quasi-ordering over the set X = {x, y, z}, with xPy, ¬xRz, ¬zRx, ¬yRz, ¬zRy. What is the maximal set? What is the choice set? 2. Supose that a choice function C(⋅) satisfies both contraction consistency (α) and expansion consistency (β). Define R as follows: xRy iff x ∈ C({x, y}). Prove that R is transitive. 3. Daniel Kahneman and Amos Tversky find that most people prefer a certain payoff of $3000 to a lottery that offers them an 80% chance of winning $4000 (otherwise winning $0), but would also prefer a lottery that offers them a 20% chance of winning $4000 (otherwise $0) to a lottery that offers them a 25% chance of winning $3000 (otherwise $0). Prove,

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