If n(A) = 82 and n(B) = 63, what is the maximum possible value of n(A ∩ B)?
Answer and explanation
Correct answer: 63
The intersection A ∩ B contains only elements that belong to both sets, so it cannot contain more elements than either A or B. Consequently, n(A ∩ B) ≤ min(n(A), n(B)) = min(82, 63) = 63. This maximum is possible when every element of B is also an element of A, meaning B is a subset of A. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
63
Why is this the correct answer?
The intersection A ∩ B contains only elements that belong to both sets, so it cannot contain more elements than either A or B. Consequently, n(A ∩ B) ≤ min(n(A), n(B)) = min(82, 63) = 63. This maximum is possible when every element of B is also an element of A, meaning B is a subset of A. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
