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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 20

If U = {1, 2, 3, 4, 5} and Aᶜ = {2, 5}, what is A ∩ Aᶜ?

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Answer and explanation

Correct answer: ∅

By definition, Aᶜ consists of the elements of U that are not members of A. Thus A and Aᶜ are disjoint sets: they cannot have a common element. This gives the universal identity A ∩ Aᶜ = ∅. Although {2, 5} is Aᶜ and {1, 3, 4} is A, neither set is their intersection. Therefore option A is correct.

Tags

setscomplementintersectiondisjoint setsComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

∅

Why is this the correct answer?

By definition, Aᶜ consists of the elements of U that are not members of A. Thus A and Aᶜ are disjoint sets: they cannot have a common element. This gives the universal identity A ∩ Aᶜ = ∅. Although {2, 5} is Aᶜ and {1, 3, 4} is A, neither set is their intersection. Therefore option A is 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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