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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 20

If A ⊆ B for sets A and B in a universal set U, which statement about their complements is correct?

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Answer and explanation

Correct answer: B′ ⊆ A′

If A ⊆ B, every element of A is also in B. Consider an element of B′: it is not in B. Since every element of A would have to be in B, that element cannot be in A either; therefore it belongs to A′. Thus every element of B′ is in A′, giving B′ ⊆ A′. Taking complements reverses the direction of inclusion.

Tags

setscomplementsubset relationset inclusionproperties of setsMathematicsComplement of a Set and Its PropertiesClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

B′ ⊆ A′

Why is this the correct answer?

If A ⊆ B, every element of A is also in B. Consider an element of B′: it is not in B. Since every element of A would have to be in B, that element cannot be in A either; therefore it belongs to A′. Thus every element of B′ is in A′, giving B′ ⊆ A′. Taking complements reverses the direction of inclusion.

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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