If n(A ∪ B) = n(U), which region is empty in the Venn diagram?
Answer and explanation
Correct answer: (A ∪ B)'
The universal set U contains every element under consideration. If n(A ∪ B) = n(U), then A ∪ B contains all elements of U. Therefore, no element lies outside A ∪ B, so its complement (A ∪ B)' is the empty set. The intersection and the two difference regions may still contain elements; the given condition only guarantees that the outside region is empty.
Frequently asked questions
What is the correct answer to this question?
(A ∪ B)'
Why is this the correct answer?
The universal set U contains every element under consideration. If n(A ∪ B) = n(U), then A ∪ B contains all elements of U. Therefore, no element lies outside A ∪ B, so its complement (A ∪ B)' is the empty set. The intersection and the two difference regions may still contain elements; the given condition only guarantees that the outside region is empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
