If only A has 31 elements, only B has 27 elements, only C has 25 elements, the total of the exactly-two-set regions is 42, and all three sets have 11 elements, then what is n(A ∪ B ∪ C)?
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Answer and explanation
Correct answer: 136
The union contains every disjoint Venn-diagram region exactly once. Therefore, add the three only-set regions, the total of the exactly-two-set regions, and the three-set intersection: 31 + 27 + 25 + 42 + 11 = 136. Since these regions do not overlap, no subtraction or repeated counting is required.
Frequently asked questions
What is the correct answer to this question?
136
Why is this the correct answer?
The union contains every disjoint Venn-diagram region exactly once. Therefore, add the three only-set regions, the total of the exactly-two-set regions, and the three-set intersection: 31 + 27 + 25 + 42 + 11 = 136. Since these regions do not overlap, no subtraction or repeated counting is required.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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