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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 10

If A ∪ B = A and A \ B = ∅, which conclusion is correct?

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Answer and explanation

Correct answer: A = B

The equality A ∪ B = A means that every element of B is already in A, so B ⊆ A. The condition A \ B = ∅ means that no element of A lies outside B; therefore A ⊆ B. Since each set is a subset of the other, the two sets are equal. Hence A = B, and no claim that either set is empty is justified.

Tags

setsequalityuniondifferenceOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A = B

Why is this the correct answer?

The equality A ∪ B = A means that every element of B is already in A, so B ⊆ A. The condition A \ B = ∅ means that no element of A lies outside B; therefore A ⊆ B. Since each set is a subset of the other, the two sets are equal. Hence A = B, and no claim that either set is empty is justified.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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