If n(A∩(B∪C))=52, only A∩B has 23 elements and only A∩C has 18 elements, what is n(A∩B∩C)?
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Answer and explanation
Correct answer: 11
By distributivity, A∩(B∪C)=(A∩B)∪(A∩C). The stated region contains three disjoint parts: the A∩B-only region with 23 elements, the A∩C-only region with 18 elements, and the central triple intersection with x elements. Therefore 52=23+18+x, so x=11. Hence option A is correct; 41 is only the sum of the two exclusive parts.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
By distributivity, A∩(B∪C)=(A∩B)∪(A∩C). The stated region contains three disjoint parts: the A∩B-only region with 23 elements, the A∩C-only region with 18 elements, and the central triple intersection with x elements. Therefore 52=23+18+x, so x=11. Hence option A is correct; 41 is only the sum of the two exclusive parts.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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