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theorymidterm - Name Midterm Exam Econ 210A UCSB Nov 5 2007...

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Name Midterm Exam, Econ 210A, UCSB, Nov 5, 2007 Try to answer five of the six questions, including Question 6. 1) Suppose that the preference relation R is complete and transitive. We define the relation P such that xPy if and only if xRy and not yRx . a) Is P transitive? If so, prove it. If not give a counterexample by showing a transitive, complete R for which P is not transitive. b) Is P complete? If so, prove it. If not give a counterexample by showing a transitive, complete R for which P is not complete. 1
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2) Define the relation P on the real line, so that for any two points x and y on the line, xPy if and only if x - y > 1. Is P transitive? Prove it if true. Show a counterexample if false. Suppose that we define the relation R on the real line so that xRy if and only if not xPy . Is R transitive? Prove it if true. Show a counterexample if false. 2
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3) Define each of the following. Use a full grammatical sentence in your defini- tion.
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