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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesHardLevel 19

If A ⊆ B ⊆ U, which relation is always true?

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Answer and explanation

Correct answer: Bᶜ ⊆ Aᶜ

Taking complements reverses the direction of set inclusion. Since every element of A is in B, any element that is not in B is certainly not in A. Therefore every element of Bᶜ belongs to Aᶜ, giving Bᶜ ⊆ Aᶜ. Equality is not guaranteed unless A and B are equal, so option B is the only always-true statement.

Tags

setscomplementsubsetinclusion-reversalComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

Bᶜ ⊆ Aᶜ

Why is this the correct answer?

Taking complements reverses the direction of set inclusion. Since every element of A is in B, any element that is not in B is certainly not in A. Therefore every element of Bᶜ belongs to Aᶜ, giving Bᶜ ⊆ Aᶜ. Equality is not guaranteed unless A and B are equal, so option B is the only always-true statement.

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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