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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 21

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

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Answer and explanation

Correct answer: C′ ⊆ B′ ⊆ A′

Taking complements reverses the direction of inclusion. Since every element of A is in B and every element of B is in C, any element outside C is certainly outside B and outside A. Therefore C′ ⊆ B′ ⊆ A′. Equality is not guaranteed because the original inclusions may be proper.

Tags

setssubsetscomplementorder-reversalComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

C′ ⊆ B′ ⊆ A′

Why is this the correct answer?

Taking complements reverses the direction of inclusion. Since every element of A is in B and every element of B is in C, any element outside C is certainly outside B and outside A. Therefore C′ ⊆ B′ ⊆ A′. Equality is not guaranteed because the original inclusions may be proper.

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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