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Class 10MathematicsSetsComplement of a Set and Its PropertiesEasyLevel 20

If A − B = ∅, which conclusion is always correct?

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Answer and explanation

Correct answer: A ⊆ B

The difference A − B consists of elements that belong to A but do not belong to B; equivalently, A − B = A ∩ B'. If this set is empty, there is no element of A outside B. Therefore every element of A must be in B, which is exactly the statement A ⊆ B. The other conclusions do not necessarily follow.

Tags

setsset differencecomplementsubsetComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A ⊆ B

Why is this the correct answer?

The difference A − B consists of elements that belong to A but do not belong to B; equivalently, A − B = A ∩ B'. If this set is empty, there is no element of A outside B. Therefore every element of A must be in B, which is exactly the statement A ⊆ B. The other conclusions do not necessarily follow.

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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