If n(U)=160 and n(A∪B∪C)=127, how many elements belong to none of the three sets?
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Answer and explanation
Correct answer: 33
The universal set U contains 160 elements. The union A∪B∪C contains every element belonging to at least one of the three sets, namely 127 elements. The remaining elements belong to none of them, so they form the complement of the union. Therefore, n((A∪B∪C)′)=n(U)−n(A∪B∪C)=160−127=33.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
The universal set U contains 160 elements. The union A∪B∪C contains every element belonging to at least one of the three sets, namely 127 elements. The remaining elements belong to none of them, so they form the complement of the union. Therefore, n((A∪B∪C)′)=n(U)−n(A∪B∪C)=160−127=33.
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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