1) Let R be the relation defined on N N as follows: (m, n)R(p, q) if and only if m – pis divisible by 3 and n – q is divisible by 5. For example, (2, 19)R(8,4). 1. Identify two elements of N X N which are related under R to (6, 45). II. Is R reflexive? Justify your answer. III. Is R symmetric? Justify your answer. IV. Is R transitive? Justify your answer. V.Is R an equivalence relation? Justify your answer. 2) Let T be the relation on N given by xTy x < y Prove that T is a partial order but not an equivalence relation.
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