6. Let A and B be two subsets of a metric space X (a) Show that...

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6. Let A and B be two subsets of a metric space X (a) Show that if A is open then An B C AN B. Give an example where the inclusion is strict (b) Suppose that A and B are open. Prove that the following three conditions are equivalent. i. AnB= 0 ii. AnB=0 iii. AnB = 0 %3D 6. Let A and B be two subsets of a metric space X (a) Show that if A is open then An B C AN B. Give an example where the inclusion is strict (b) Suppose that A and B are open. Prove that the following three conditions are equivalent. i. AnB= 0 ii. AnB=0 iii. AnB = 0 %3D