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1: For each the following groups of sets, determine whether they form a partition for the set of integers. Explain your answer.
a. A1 = {n ? Z : n > 0}
A2 = {n ? Z : n < 0}
They do not form a partition because A1 nor A2 include 0 which is in the set of integers, A1 is > 0 and A2 is < 0.
b. B1 = {n ? Z : n = 2k, for some integer k}
B?2 = {n ? Z : n = 2k + 1, for some integer k}
B3 = {n ? Z : n = 3k, for some integer k}
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