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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If A' ∩ B' = ∅, what is the correct conclusion about A ∪ B?

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Answer and explanation

Correct answer: A ∪ B = U

By De Morgan's law, A' ∩ B' = (A ∪ B)'. The condition says that the complement of A ∪ B is empty. A set has an empty complement in U only when it contains every element of U. Therefore, A ∪ B = U, so option B is correct. Equivalently, every element of the universal set belongs to A or to B.

Tags

setscomplementsDe-Morgan-lawsuniversal-setComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A ∪ B = U

Why is this the correct answer?

By De Morgan's law, A' ∩ B' = (A ∪ B)'. The condition says that the complement of A ∪ B is empty. A set has an empty complement in U only when it contains every element of U. Therefore, A ∪ B = U, so option B is correct. Equivalently, every element of the universal set belongs to A or to B.

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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