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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

From the statements A ∩ Aᶜ = ∅ and A ∪ Aᶜ = U, which conclusion follows?

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Answer and explanation

Correct answer: A and Aᶜ form a partition of U

A partition of U consists of non-overlapping subsets whose union is U. The equation A ∩ Aᶜ = ∅ shows that A and its complement are disjoint, while A ∪ Aᶜ = U shows that together they contain every element of U. Thus A and Aᶜ form a partition of U, making option A correct.

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setscomplementpartitiondisjoint-setsComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A and Aᶜ form a partition of U

Why is this the correct answer?

A partition of U consists of non-overlapping subsets whose union is U. The equation A ∩ Aᶜ = ∅ shows that A and its complement are disjoint, while A ∪ Aᶜ = U shows that together they contain every element of U. Thus A and Aᶜ form a partition of U, 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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