If n(U)=110 and n(A∪B∪C)=92, how many elements belong to none of the sets?
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Answer and explanation
Correct answer: 18
The elements belonging to none of A, B, or C are precisely the elements in the complement of their union within the universal set. Hence n((A∪B∪C)ᶜ)=n(U)−n(A∪B∪C). Substituting the given values gives 110−92=18. Therefore, 18 elements lie outside all three sets, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The elements belonging to none of A, B, or C are precisely the elements in the complement of their union within the universal set. Hence n((A∪B∪C)ᶜ)=n(U)−n(A∪B∪C). Substituting the given values gives 110−92=18. Therefore, 18 elements lie outside all three sets, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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