Let d be a metric on X. The distance between an element p E X and a nonempt; subset AC X is defined by d(p, A) = inf{d(p, a)la E A}. Similarly, the distance between two subsets A, BC X is defined by d(A, B) = inf{d(a, b)|a E A, b e B}. (a) Show that if An B+0, then d(A, B) = 0. (b) Show: Let B be a nonempty subset of X. If x, y E X, then |d(x, B) – d(y, b)| < d(x, y).

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A: Discrete metric space.

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