If n(U) = 40 and n(A ∪ B) = 26, what is the number of elements in neither A nor B?
Answer and explanation
Correct answer: 14
The union A ∪ B contains every element that belongs to A, to B, or to both. Therefore, the elements belonging to neither set are outside the union but still inside the universal set U. Subtract the union count from the universal-set count: n(U) − n(A ∪ B) = 40 − 26 = 14. Hence, option A is correct. In a Venn diagram, this is the region inside the rectangle but outside both circles.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The union A ∪ B contains every element that belongs to A, to B, or to both. Therefore, the elements belonging to neither set are outside the union but still inside the universal set U. Subtract the union count from the universal-set count: n(U) − n(A ∪ B) = 40 − 26 = 14. Hence, option A is correct. In a Venn diagram, this is the region inside the rectangle but outside both circles.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
