Unformatted text preview: Instead, use the binomial theorem and any mod rules you deem necessary. 5) If A ={ 1, 2, 3, 4, 5, 6, 7, 8 }, determine the number of relations on A that are (a) reflexive; (b) symmetric; (c) reflexive and symmetric; (d) reflexive and contain ( 1 , 2 ); (e) symmetric and contain ( 1 , 2 ); (f) antisymmetric; (g) antisymmetric and contain ( 1 , 2 ); (h) symmetric and antisymmetric; (i) reflexive, symmetric and antisymmetric. 6) Prove or disprove: Let R be a relation over A x A. If R ° R is transitive, then R is transitive as well. 7) Consider the following relation R defined over the set of positive integers: R = {(x,y)  x/y = 4 ∨ y/x = 4} Determine if the relation R is (i)reflexive, (ii)irreflexive, (iii)symmetric, (iv)antisymmetric, and (v)transitive....
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 Spring '09
 Natural number, Greatest common divisor, Euclidean algorithm, prime Factorization, Euclidean domain

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