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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 20

If n(U) = 25, what is n(A ∪ Aᶜ)?

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Answer and explanation

Correct answer: 25

Every element of the universal set U is either an element of A or an element of its complement Aᶜ. Consequently, A ∪ Aᶜ = U. Taking cardinalities on both sides gives n(A ∪ Aᶜ) = n(U) = 25. Therefore option A is correct. The result does not depend on the particular elements or size of A.

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setscomplementunionuniversal setComplement 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?

Every element of the universal set U is either an element of A or an element of its complement Aᶜ. Consequently, A ∪ Aᶜ = U. Taking cardinalities on both sides gives n(A ∪ Aᶜ) = n(U) = 25. Therefore option A is correct. The result does not depend on the particular elements or size of A.

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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