If n(U) = 190, n(A) = 74, and n(B) = 91, what is the maximum possible value of n(A ∩ B)?
Answer and explanation
Correct answer: 74
The intersection A ∩ B consists only of elements that are in A, so it cannot contain more elements than A. It also cannot contain more elements than B; therefore, n(A ∩ B) ≤ min(n(A), n(B)). Here, min(74, 91) = 74. This maximum is attainable by taking A as a subset of B, while the remaining elements of B lie outside A. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
74
Why is this the correct answer?
The intersection A ∩ B consists only of elements that are in A, so it cannot contain more elements than A. It also cannot contain more elements than B; therefore, n(A ∩ B) ≤ min(n(A), n(B)). Here, min(74, 91) = 74. This maximum is attainable by taking A as a subset of B, while the remaining elements of B lie outside A. Hence, option B is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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