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Question: 6. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5. (a) What are the smallest and largest possible values of |A ∪ B|? Explain. (b) What are the smallest and largest possible values of |A ∩ B|? Explain. (c) What are the smallest and largest possible values of |A × B|? Explain.

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a) The smallest possible value of |A ∪ B| is 7, because no matter what elements are contained in B, it will always add at least one new element to A. The largest possible value of |A ∪ B| is 9, since at most, four elements of B can be used to supplement A without any being repeated. b) The smallest possible value of |A ∩ B| is 0, because no matter what elements are contained in B, there is always the possibility that none of them are elements of A. The largest possible value of |A ∩ B| is 4, since at most, all four elements of A can be contained in B without any repetition occuring. c) The smallest possible value of |A × B| is 0, because no matter what elements are contained in B, there is always the possibility that none of them are related to any elements of A. The largest possible value of |A × B| is 20, since at most, all four elements of A can be related to each of the five elements in B without any repetition occuring.

Feb. 9, 2023, 6:43 p.m.

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