Prove that each of the properties in parts (a)–(d) holds whenever A and B are finite sets.a) J(A, A) = 1 and dJ (A, A) = 0b) J(A, B) = J(B, A) and dJ (A, B) = dJ (B, A)c) J(A, B) = 1 and dJ (A, B) = 0 if and only if A = Bd) 0 ≤ J(A, B) ≤ 1 and 0 ≤ dJ (A, B) ≤ 1e) Show that if A, B, and C are sets, then dJ (A,C) ≤ dJ (A, B) + dJ (B,C). (This inequality is known as the triangle inequality and together with parts (a), (b), and (c) implies that dJ is a metric.)

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