If n(U) = 150, n(A) = 66, and n(B) = 59, what is the maximum possible value of n(A ∩ B)?
Answer and explanation
Correct answer: 59
The intersection A ∩ B consists of elements that belong to both A and B. It cannot contain more elements than the smaller of the two sets, because every common element must be an element of B as well as A. Therefore, n(A ∩ B) ≤ min(n(A), n(B)) = min(66, 59) = 59. This maximum is attainable by placing all 59 elements of B inside A, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
59
Why is this the correct answer?
The intersection A ∩ B consists of elements that belong to both A and B. It cannot contain more elements than the smaller of the two sets, because every common element must be an element of B as well as A. Therefore, n(A ∩ B) ≤ min(n(A), n(B)) = min(66, 59) = 59. This maximum is attainable by placing all 59 elements of B inside A, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
