In three sets, only A=23, only B=27, only C=21, only A∩B=13, only B∩C=11, only C∩A=9, and A∩B∩C=7. What is n((A∪B∪C)ᶜ) if n(U)=130?
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Answer and explanation
Correct answer: 19
The seven listed regions are disjoint and together form A∪B∪C. Their total is 23+27+21+13+11+9+7=111. The complement contains the universal-set elements outside this union. Hence n((A∪B∪C)ᶜ)=n(U)−n(A∪B∪C)=130−111=19. The triple intersection is counted once because it is given as its own region.
Frequently asked questions
What is the correct answer to this question?
19
Why is this the correct answer?
The seven listed regions are disjoint and together form A∪B∪C. Their total is 23+27+21+13+11+9+7=111. The complement contains the universal-set elements outside this union. Hence n((A∪B∪C)ᶜ)=n(U)−n(A∪B∪C)=130−111=19. The triple intersection is counted once because it is given as its own region.
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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