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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If A ⊆ B in a universal set U, which of the following relations is always true?

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Answer and explanation

Correct answer: B′ ⊆ A′

A ⊆ B means that every element of A is also an element of B. Consider any element x in B′. Since x is not in B, it cannot be in A either; otherwise A ⊆ B would force x to be in B. Therefore x belongs to A′, proving B′ ⊆ A′. Taking complements reverses the direction of inclusion, so option A is correct.

Tags

setscomplementsubsetinclusion reversalComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

B′ ⊆ A′

Why is this the correct answer?

A ⊆ B means that every element of A is also an element of B. Consider any element x in B′. Since x is not in B, it cannot be in A either; otherwise A ⊆ B would force x to be in B. Therefore x belongs to A′, proving B′ ⊆ A′. Taking complements reverses the direction of inclusion, so 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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