In a Venn diagram, n(A ∪ B ∪ C) = 190 and n((A ∪ B ∪ C)′) = 25. What is n(U)?
Answer and explanation
Correct answer: 215
The universal set U consists of all elements that lie inside A ∪ B ∪ C and all elements outside that union. The complement (A ∪ B ∪ C)′ contains 25 elements, while the union contains 190 elements. These two disjoint regions together make the whole universal set. Therefore n(U) = n(A ∪ B ∪ C) + n((A ∪ B ∪ C)′) = 190 + 25 = 215. The information about exactly two sets is not needed.
Frequently asked questions
What is the correct answer to this question?
215
Why is this the correct answer?
The universal set U consists of all elements that lie inside A ∪ B ∪ C and all elements outside that union. The complement (A ∪ B ∪ C)′ contains 25 elements, while the union contains 190 elements. These two disjoint regions together make the whole universal set. Therefore n(U) = n(A ∪ B ∪ C) + n((A ∪ B ∪ C)′) = 190 + 25 = 215. The information about exactly two sets is not needed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
