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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 20

Which of the following statements about the complement Aᶜ of a set A is always true?

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Answer and explanation

Correct answer: A ∪ Aᶜ = U

The complement Aᶜ consists of all elements of the universal set U that are not in A. Every element of U is therefore either in A or in Aᶜ, so their union is U: A ∪ Aᶜ = U. They have no common element, which means A ∩ Aᶜ = ∅. Thus options B, C, and D are not generally true.

Tags

setscomplementuniversal setset identitiesunionintersectionComplement of a Set and Its PropertiesMathematics

Frequently asked questions

What is the correct answer to this question?

A ∪ Aᶜ = U

Why is this the correct answer?

The complement Aᶜ consists of all elements of the universal set U that are not in A. Every element of U is therefore either in A or in Aᶜ, so their union is U: A ∪ Aᶜ = U. They have no common element, which means A ∩ Aᶜ = ∅. Thus options B, C, and D are not generally 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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