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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 the union of two sets includes all the elements from each set. The largest possible value of |A ∪ B| is 9, because the union of two sets cannot exceed the sum of their cardinalities. (b) The smallest possible value of |A ∩ B| is 0, because the intersection of two sets is the set of elements that they have in common. The largest possible value of |A ∩ B| is 4, because the intersection of two sets cannot exceed the minimum of their cardinalities. (c) The smallest possible value of |A × B| is 0, because the product of two sets is the set of ordered pairs of elements from the two sets. The largest possible value of |A × B| is 40, because the product of two sets cannot exceed the product of their cardinalities.

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

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