If n(A) = 46 and n(B) = 39, what is the maximum possible value of n(A ∩ B)?
Answer and explanation
Correct answer: 39
The intersection A ∩ B contains elements common to both sets, so its cardinality cannot be greater than the cardinality of either set. Therefore, n(A ∩ B) ≤ min[n(A), n(B)] = min(46, 39) = 39. This maximum is attainable when every element of the smaller set B is also an element of A, so B is completely contained in A.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
The intersection A ∩ B contains elements common to both sets, so its cardinality cannot be greater than the cardinality of either set. Therefore, n(A ∩ B) ≤ min[n(A), n(B)] = min(46, 39) = 39. This maximum is attainable when every element of the smaller set B is also an element of A, so B is completely contained in A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
