If n(A) = 39, n(B) = 50, and the number of elements only in B, that is, not in A, is 28, what is n(A ∩ B)?
Answer and explanation
Correct answer: 22
The set B consists of two disjoint regions: the elements only in B and the elements in the intersection A ∩ B. Thus n(B) = n(B − A) + n(A ∩ B). Since n(B) = 50 and n(B − A) = 28, the common part is n(A ∩ B) = 50 − 28 = 22. Therefore option B is correct. The value 28 describes only B, while 50 describes all of B.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The set B consists of two disjoint regions: the elements only in B and the elements in the intersection A ∩ B. Thus n(B) = n(B − A) + n(A ∩ B). Since n(B) = 50 and n(B − A) = 28, the common part is n(A ∩ B) = 50 − 28 = 22. Therefore option B is correct. The value 28 describes only B, while 50 describes all of B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
