If n(U)=100, n(A)=45, n(B)=40, and n(A∩B)=15, what is n((A∪B)′)?
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Answer and explanation
Correct answer: 30
First apply the inclusion-exclusion formula: n(A∪B)=n(A)+n(B)−n(A∩B)=45+40−15=70. The complement of A∪B contains all elements of U outside both sets. Therefore n((A∪B)′)=n(U)−n(A∪B)=100−70=30. Option C is the union size, not its complement, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
First apply the inclusion-exclusion formula: n(A∪B)=n(A)+n(B)−n(A∩B)=45+40−15=70. The complement of A∪B contains all elements of U outside both sets. Therefore n((A∪B)′)=n(U)−n(A∪B)=100−70=30. Option C is the union size, not its complement, so option A 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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