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Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy

1. 3 ≤ n(A ∪ B) ≤ 6
2. 3 ≤ n(A ∪ B) ≤ 9
3. 6 ≤ n(A ∪ B) ≤ 9
4. 0 ≤ n(A ∪ B) ≤ 9

Correct answer: 6 ≤ n(A ∪ B) ≤ 9

Solution

The union of sets A and B can have a minimum of 6 elements if all elements of A are also in B, and a maximum of 9 elements if all elements are distinct. Therefore, the cardinality of the union must fall within the range of 6 to 9.

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