If n(A) = 73 and n(B) = 58, what is the maximum possible value of n(A ∩ B)?
Advertisement
Answer and explanation
Correct answer: 58
The intersection A ∩ B consists only of elements common to both sets. Therefore, it cannot contain more elements than either set, so n(A ∩ B) ≤ min(73, 58) = 58. This value is attainable if every element of B is also in A, meaning B is a subset of A. Hence the maximum is 58.
Frequently asked questions
What is the correct answer to this question?
58
Why is this the correct answer?
The intersection A ∩ B consists only of elements common to both sets. Therefore, it cannot contain more elements than either set, so n(A ∩ B) ≤ min(73, 58) = 58. This value is attainable if every element of B is also in A, meaning B is a subset of A. Hence the maximum is 58.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
Advertisement