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1 Prove that the empty set is a subset of every set Let A, A2, A.... be subsets of a metric space. (a) If

1 Prove that the empty set is a subset of every set Let A, A2, A.... be subsets of a metric space. (a) If B.= U7, A., prove that B. U., A, for n=1, 2, 3, .... (b) If BU A., prove that B U... .. Show, by an example, that this inclusion can be proper.

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