In a three-set Venn diagram, only B = 17, only A ∩ B = 9, only B ∩ C = 11, and A ∩ B ∩ C = 6. What is n(B)?
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Answer and explanation
Correct answer: 43
The cardinality n(B) is obtained by adding all mutually exclusive regions contained in B. These are the region only in B, the region only in A ∩ B, the region only in B ∩ C, and the central triple-intersection region. Therefore, n(B) = 17 + 9 + 11 + 6 = 43. No region outside B should be counted.
Frequently asked questions
What is the correct answer to this question?
43
Why is this the correct answer?
The cardinality n(B) is obtained by adding all mutually exclusive regions contained in B. These are the region only in B, the region only in A ∩ B, the region only in B ∩ C, and the central triple-intersection region. Therefore, n(B) = 17 + 9 + 11 + 6 = 43. No region outside B should be counted.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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