If only A, only B, only C, exactly two sets, and all three sets contain 16, 19, 14, 27, and 8 elements respectively, how many elements are in at least one set?
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Answer and explanation
Correct answer: 84
“At least one set” means the union A∪B∪C. The given categories are mutually exclusive Venn-diagram regions: only A, only B, only C, exactly two sets, and all three sets. Hence every element in the union is counted exactly once. Therefore, n(A∪B∪C)=16+19+14+27+8=84, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
84
Why is this the correct answer?
“At least one set” means the union A∪B∪C. The given categories are mutually exclusive Venn-diagram regions: only A, only B, only C, exactly two sets, and all three sets. Hence every element in the union is counted exactly once. Therefore, n(A∪B∪C)=16+19+14+27+8=84, so 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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