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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If A ∪ B′ = U, which relation is always true?

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Answer and explanation

Correct answer: B ⊆ A

Take the complement of both sides of A ∪ B′ = U. Using De Morgan’s law, (A ∪ B′)′ = A′ ∩ B, while U′ = ∅. Hence A′ ∩ B = ∅, which means that no element of B lies outside A. Therefore every element of B belongs to A, so B ⊆ A. Equality or disjointness is not required, making option A correct.

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setscomplementDe Morgan lawsubsetComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

B ⊆ A

Why is this the correct answer?

Take the complement of both sides of A ∪ B′ = U. Using De Morgan’s law, (A ∪ B′)′ = A′ ∩ B, while U′ = ∅. Hence A′ ∩ B = ∅, which means that no element of B lies outside A. Therefore every element of B belongs to A, so B ⊆ A. Equality or disjointness is not required, making option A 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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