1. For each of the following relations, determine whether it is (a) reflexive, (b) symmetric, (c) transitive, and prove your claims. (i) On the set of natural numbers N, with the relation R = {(a, b) E N x N: gcd(a, b) = 1}. (ii) On R, with xy if |x|+|y| = |x+y|. (iii) On Zx Z, with (x1, y1)~ (x2, Y2) if x₁ = x2 or y₁ = y2. A I

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