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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 21

If U = {a, b, c, d, e, f}, A = {a, b, c}, and D = {d, e, f}, which conclusion is correct using A ∩ D and A ∪ D?

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Answer and explanation

Correct answer: D = Aᶜ

The sets A and D have no common elements, so A ∩ D = ∅. Together they contain every element of U, so A ∪ D = U. A set that is disjoint from A and whose union with A is U is precisely the complement of A. Therefore, D = Aᶜ.

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setsintersectionunioncomplementComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

D = Aᶜ

Why is this the correct answer?

The sets A and D have no common elements, so A ∩ D = ∅. Together they contain every element of U, so A ∪ D = U. A set that is disjoint from A and whose union with A is U is precisely the complement of A. Therefore, D = Aᶜ.

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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