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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 16

If \(A-B=B-A\), which conclusion is correct?

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Answer and explanation

Correct answer: \(A=B\)

Suppose an element belongs to A but not B. It would then belong to \(A-B\), but not to \(B-A\), contradicting equality. Similarly, an element belonging to B but not A would occur only in \(B-A\). Hence neither set can have an element absent from the other, so every element is common and \(A=B\).

Tags

setsset differenceequalitylogical reasoningset identitiesOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

\(A=B\)

Why is this the correct answer?

Suppose an element belongs to A but not B. It would then belong to \(A-B\), but not to \(B-A\), contradicting equality. Similarly, an element belonging to B but not A would occur only in \(B-A\). Hence neither set can have an element absent from the other, so every element is common and \(A=B\).

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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