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nottrans

nottrans - B Show by example that if ± is transitive but...

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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. Define ± 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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