The smallest and largest possible values of |A ∪ B| are 2, 4, and 6. The smallest and largest possible values of |A ∩ B| are 1, 0, and 1. The smallest and largest possible values of |A × B| are 6, 10, and 16.

The smallest possible value of |A ∪ B| is 2 because there are two elements in A and there are six elements in B. The largest possible value of |A ∪ B| is 16 because there are two elements in A and t

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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 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.

Answered by text-davinci-003

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

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6. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5. The smallest possible value of |A ∪ B| is 2, and the largest possible value is 8. The smallest possible value of |A ∩ B| is 1, and the largest

6. Let A = {2, 4, 6, 8}. Suppose B is a set with |B| = 5. (a) The smallest possible value of |A ∪ B| is 2. The largest possible value of |A ∪ B| is 8. (b) The smallest possible value of |A ∩ B| is

(a) A ∩ B = {x ∈ N : 3 ≤ x ≤ 13} (b) A ∪ B = {x ∈ N : x is even} (c) B ∩ C = {x ∈ N : x is odd} (d) B ∪ C = {x ∈ N : x is even or x is odd}

5. Let A = {x ∈ N : 3 ≤ x ≤ 13}, B = {x ∈ N : x is even}, and C = {x ∈ N : x is odd}. Find A ∩ B. Find A ∪ B. Find B ∩ C. Find B ∪ C.

cardinality of each of the sets

(a) The set of all integers whose absolute value is at most 5. (b) The set of all natural numbers strictly between 1 and 10.

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Published: Thursday, February 9, 2023

The smallest possible value of |A ∪ B| is 2 because there are two elements in A and there are six elements in B. The largest possible value of |A ∪ B| is 16 because there are two elements in A and t

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