If only A=11, only B=13, only C=9, only (A∩B)=5, only (B∩C)=4, only (C∩A)=6, and A∩B∩C=3, what is n(A∪B∪C)?
Answer and explanation
Correct answer: 51
The wording “only” is important: each of the first six values represents a separate Venn-diagram region, and the final value represents the central region common to all three sets. Every element in the union belongs to exactly one of these seven disjoint regions. Therefore, n(A∪B∪C)=11+13+9+5+4+6+3=51. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
51
Why is this the correct answer?
The wording “only” is important: each of the first six values represents a separate Venn-diagram region, and the final value represents the central region common to all three sets. Every element in the union belongs to exactly one of these seven disjoint regions. Therefore, n(A∪B∪C)=11+13+9+5+4+6+3=51. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
