nottrans

nottrans - B) Show by example that if is transitive but not...

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Homework Problem 1 Let ± be a binary relation on X . Consider the relation P on X defined so that xPy if and only if NOT y ± x . A) If ± is transitive and complete, show that P must be transitive. B) Give an example to show that if ± is transitive and complete, the relation P is not necessarily complete.
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Unformatted text preview: B) Show by example that if is transitive but not complete, the relation P is not necessarily transitive. Hint: Let X be the Euclidean plane. Dene so that ( x 1 ,x 2 ) ( y 1 ,y 2 ) if and only if x 1 y 1 and x 2 y 2 . 1...
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This note was uploaded on 12/25/2011 for the course ECON 210A taught by Professor Bergstrom during the Fall '09 term at UCSB.

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