If n(A)=28, n(B)=30 and only B has 21 elements, meaning 21 elements are not in A, what is n(A∩B)?
Answer and explanation
Correct answer: 9
The set B consists of its exclusive part, containing elements in B but not A, and its common part, A∩B. Therefore n(B)=n(B\A)+n(A∩B). The given values give 30=21+n(A∩B), so n(A∩B)=30−21=9. Option B is correct. The value 21 counts only-B elements, while 30 counts all elements of B, so neither is the intersection.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The set B consists of its exclusive part, containing elements in B but not A, and its common part, A∩B. Therefore n(B)=n(B\A)+n(A∩B). The given values give 30=21+n(A∩B), so n(A∩B)=30−21=9. Option B is correct. The value 21 counts only-B elements, while 30 counts all elements of B, so neither is the intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
