In three sets, only A = 20, only A ∩ B = 8, only C ∩ A = 6, and A ∩ B ∩ C = 5. What is n(A)?
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Answer and explanation
Correct answer: 39
To find n(A), include every Venn-diagram region that lies inside set A. These regions are the part only in A, the part only in A ∩ B, the part only in C ∩ A, and the central part A ∩ B ∩ C. Hence n(A) = 20 + 8 + 6 + 5 = 39. Regions that lie outside A are not included in the cardinality of A.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
To find n(A), include every Venn-diagram region that lies inside set A. These regions are the part only in A, the part only in A ∩ B, the part only in C ∩ A, and the central part A ∩ B ∩ C. Hence n(A) = 20 + 8 + 6 + 5 = 39. Regions that lie outside A are not included in the cardinality of 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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