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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 21

If 6 ∈ U and 6 ∉ A, which conclusion is correct?

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Answer and explanation

Correct answer: 6 ∈ Aᶜ

The complement Aᶜ of A with respect to U is defined as Aᶜ = U \ A. Thus, an element belongs to Aᶜ precisely when it belongs to U but does not belong to A. The given facts state that 6 is in U and is not in A, so 6 must be in Aᶜ. It cannot simultaneously belong to A and Aᶜ, because A ∩ Aᶜ = ∅.

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setscomplementelement-membershipset logicMathematicsComplement of a Set and Its PropertiesClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

6 ∈ Aᶜ

Why is this the correct answer?

The complement Aᶜ of A with respect to U is defined as Aᶜ = U \ A. Thus, an element belongs to Aᶜ precisely when it belongs to U but does not belong to A. The given facts state that 6 is in U and is not in A, so 6 must be in Aᶜ. It cannot simultaneously belong to A and Aᶜ, because A ∩ 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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