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need help on discrete structure please 1. For each of the following relations, compute the reflexive, symmetric, and transitive closures. o divides. E.g., 2 divides

need help on discrete structure please

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1. For each of the following relations, compute the reflexive, symmetric, and transitive closures. o divides. E.g., 2 divides 4, 3 divides 15, but 2 does not divide 7 o subset o proper subset 2. Show that the relation defined by z R y (x-y) 0 (mod 3)] is an equivalence relation over the integers. What are the equivalence classes of R? 3. Consider the following relation over the non-negative rationals: Let and be two non-negative rationals in lowest terms. 92 91 P1 Show that this defines a well-ordering. Why do we have to restrict ourselves to the non- negative rationals above? l.e., give an example showing what goes wrong if we consider rationals other than the ones that are non-negative. Why do we have to say "in lowest terms"? l.e., give an example showing what goes wrong if we do not say "in lowest terms". 4. Show that the relation is not a well-ordering over the non-negative rationals

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