If n(A ∪ B ∪ C) = 135, exactly one set contains 58 elements, and exactly two sets contain 49 elements, what is n(A ∩ B ∩ C)?
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Answer and explanation
Correct answer: 28
The union of three sets is partitioned into three mutually exclusive types of regions: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Therefore, 135 = 58 + 49 + n(A ∩ B ∩ C). Solving gives n(A ∩ B ∩ C) = 135 − 58 − 49 = 28. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
The union of three sets is partitioned into three mutually exclusive types of regions: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Therefore, 135 = 58 + 49 + n(A ∩ B ∩ C). Solving gives n(A ∩ B ∩ C) = 135 − 58 − 49 = 28. 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.
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