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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 21

If A ∪ B′ = U, which of the following statements must be true?

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Answer and explanation

Correct answer: B ⊆ A

Given A ∪ B′ = U, take complements on both sides. By De Morgan’s law, (A ∪ B′)′ = A′ ∩ B, while U′ = ∅. Thus A′ ∩ B = ∅, meaning that no element of B lies outside A. Therefore every element of B belongs to A, so B ⊆ A. The other statements are not necessarily true.

Tags

setscomplementsubsetDe Morgan lawComplement 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?

Given A ∪ B′ = U, take complements on both sides. By De Morgan’s law, (A ∪ B′)′ = A′ ∩ B, while U′ = ∅. Thus A′ ∩ B = ∅, meaning that no element of B lies outside A. Therefore every element of B belongs to A, so B ⊆ A. The other statements are not necessarily true.

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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