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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 10

In a Venn diagram, n(U) = 100, n(A) = 52, n(B) = 44, and n(A ∩ B) = 21. What is n((A ∪ B)ᶜ)?

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Answer and explanation

Correct answer: 25

First find the number of elements in the union using inclusion–exclusion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 52 + 44 − 21 = 75. The complement contains all elements of the universal set that are not in the union. Hence n((A ∪ B)ᶜ) = n(U) − n(A ∪ B) = 100 − 75 = 25.

Tags

setsunioncomplementinclusion-exclusionComplement 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 find the number of elements in the union using inclusion–exclusion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 52 + 44 − 21 = 75. The complement contains all elements of the universal set that are not in the union. Hence n((A ∪ B)ᶜ) = n(U) − n(A ∪ B) = 100 − 75 = 25.

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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