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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 19

If A ⊆ U, what are A ∪ A′ and A ∩ A′, respectively?

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Answer and explanation

Correct answer: U, ∅

For every element of the universal set U, either it belongs to A or it does not belong to A. The elements not in A form A′, so combining A and A′ gives the whole universal set: A ∪ A′ = U. No element can simultaneously belong to A and its complement, so A ∩ A′ = ∅. Therefore, option A is correct.

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setscomplement identitiesunionintersectionComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

U, ∅

Why is this the correct answer?

For every element of the universal set U, either it belongs to A or it does not belong to A. The elements not in A form A′, so combining A and A′ gives the whole universal set: A ∪ A′ = U. No element can simultaneously belong to A and its complement, so A ∩ A′ = ∅. Therefore, 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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