In a Venn diagram, \(n(A-B)=18\), \(n(A\cap B)=12\), \(n(B-A)=22\), and 8 elements are outside. What is \(n(U)\)?
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Answer and explanation
Correct answer: 60
The universal set contains every disjoint region shown in the two-set Venn diagram: the A-only region has 18 elements, the intersection has 12, the B-only region has 22, and the outside region has 8. Adding all regions gives \(n(U)=18+12+22+8=60\). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
60
Why is this the correct answer?
The universal set contains every disjoint region shown in the two-set Venn diagram: the A-only region has 18 elements, the intersection has 12, the B-only region has 22, and the outside region has 8. Adding all regions gives \(n(U)=18+12+22+8=60\). Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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