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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 10

If n(U) = 110, n(A) = 58, n(B) = 47, and n(A ∩ B) = 20, what is n((A ∪ B)′)?

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Answer and explanation

Correct answer: 25

First calculate the size of the union using n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Hence n(A ∪ B) = 58 + 47 − 20 = 85. The complement of the union contains all elements of the universal set that are outside both A and B. Therefore n((A ∪ B)′) = n(U) − n(A ∪ B) = 110 − 85 = 25. Thus option A is correct.

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setsvenn-diagramsunioncomplementComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

25

Why is this the correct answer?

First calculate the size of the union using n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Hence n(A ∪ B) = 58 + 47 − 20 = 85. The complement of the union contains all elements of the universal set that are outside both A and B. Therefore n((A ∪ B)′) = n(U) − n(A ∪ B) = 110 − 85 = 25. Thus 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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