5220 PS2 - Rebecca Jones MATH 5220 PS2 Problem 1...

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Rebecca Jones MATH 5220 PS2 Problem 1: Reflexivity . 1 1 1 1 reflexive is x x b x x a that such b and a x x x x n n 2200 = = 5 2200 Symmetry x x x x b x x a that such a b b a x a x x b x x b x x a x x x b x x a x x b x x a that such b a x x x x Let n n n n n = 2200 = = 5 2200 2200 2200 2200 5 * * 0 1 , 1 * * * 1 * * 0 , * . * 2 2 1 2 1 2 1 1 1 1 1 1 1 1 So, is symmetric Transitivity Let * * * * x x and x x * * * * * * 0 , * * * * * * * * * * * * * * * * * * * * * 0 , * * 0 , * * * * 3 3 2 1 3 2 1 3 2 1 1 1 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 1 1 1 x x x x b x x a that such b b b a a a x x b b x b x x a x a a x x b x x a and x b b x b and x a x a a x x b x x a that such b a and x x b x x a that such b a x x and x x n n n n n 2200 = = 5 2200 2200 2200 5 2200 5 So, is transitive. Therefore, is an equivalence relation on N. Problem 2

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(a) (i) Let S 2200 x S,
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