In a Venn diagram, n(A∩B∩C)=7, only A∩B is 9, only B∩C is 6, only C∩A is 5, and only A is 18. What is n(A)?
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Answer and explanation
Correct answer: 39
The set A contains four disjoint regions: the region belonging only to A, the region belonging to A and B but not C, the region belonging to A and C but not B, and the central region common to all three sets. Therefore, n(A)=18+9+5+7=39. The B∩C-only region is not included because it lies outside A.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
The set A contains four disjoint regions: the region belonging only to A, the region belonging to A and B but not C, the region belonging to A and C but not B, and the central region common to all three sets. Therefore, n(A)=18+9+5+7=39. The B∩C-only region is not included because it lies outside A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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