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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 8, which is the same as the number of elements in A. The largest possible value of |A ∪ B| is 9, since B has 5 elements that could potentially be added to A. (b) The smallest possible value of |A ∩ B| is 0, since B contains elements that may not exist in A. The largest possible value of |A ∩ B| is 4, which is the same as the number of elements in A. (c) The smallest possible value of |A × B| is 0, since B could contain elements that are not related to any of the elements in A. The largest possible value of |A × B| is 40, since A contains 4 elements and B contains 5 elements, and each element in A could have a relationship with each element in B.

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

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