Determine whether each of the following collections of sets is a partition for the given set A.

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Determine whether each of the following collections of sets is a partition for the given set A. If the collection is not a partition, explain why it fails to be.
(a) A = {1, 2, 3, 4, 5, 6, 7, 8}; A1 = {4, 5, 6}, A2 = {1, 8}, A3 = {2, 3, 7}.
(b) A = {a, b, c, d, e, f, g, h}; A1 = {d, e}, A2 = {a, c, d}, A3 = {f, h}, A4 = {b, g}.
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