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Unformatted text preview: A . Prove or give a counterexample to each of the following assertions. (a) If R 1 and R 2 are symmetric, then R 1 R 2 is symmetric. [2] (b) If R 1 and R 2 are antisymmetric, then R 1 R 2 is antisymmetric. [2] (c) If R 1 R 2 is reexive, then either R 1 or R 2 is reexive. [2] (d) If R 1 R 2 is reexive, then both R 1 and R 2 are reexive. [2] 6. If A = { a, b, c, d, e, f, g } , determine the number of relations on A that are (a) reexive and symmetric. [2] (b) rexive and contain ( a, b ) and ( b, c ). [2] 7. Let R consists of all pairs ( x, y ) Z Z such that x 2 y 2 is divisible by 3. (a) Show that R is an equivalence relation. [3] (b) Determine the partition induced by R . [2] 1...
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 Spring '11
 HuangJing
 Math

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