If n(A ∩ (B ∪ C)) = 44, only (A ∩ B) contains 18 elements and only (A ∩ C) contains 16 elements, then what is n(A ∩ B ∩ C)?
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Answer and explanation
Correct answer: 10
The region A ∩ (B ∪ C) consists of three mutually exclusive parts: the elements in only A ∩ B, the elements in only A ∩ C, and the central region A ∩ B ∩ C. Therefore, 44 = 18 + 16 + n(A ∩ B ∩ C). Hence, n(A ∩ B ∩ C) = 44 − 34 = 10. The central region is counted once in this partition.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The region A ∩ (B ∪ C) consists of three mutually exclusive parts: the elements in only A ∩ B, the elements in only A ∩ C, and the central region A ∩ B ∩ C. Therefore, 44 = 18 + 16 + n(A ∩ B ∩ C). Hence, n(A ∩ B ∩ C) = 44 − 34 = 10. The central region is counted once in this partition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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