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In the problem, we are given that there is a set called B with 5 members. We are also given that there is a set called A with 2, 4, 6, 8 members. We are also given that the intersection of these two sets is 5. We are also given that the union of these two sets is 18. We are also given that the difference of these two sets is 3. That is, the smallest possible value of A ∩ B is 1 and the smallest possible value of A × B is 4.

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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.

Asked by cassidipark

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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.

Answered by text-davinci-003

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

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Published: Thursday, February 9, 2023

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