If \(A\cup B=A\cap B\), what conclusion follows?
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Answer and explanation
Correct answer: \(A=B\)
For any two sets, \(A\cap B\subseteq A\cup B\). If the union and intersection are equal, every element in the union must also lie in the intersection. Thus any element belonging to A must belong to B, giving \(A\subseteq B\); similarly, \(B\subseteq A\). Therefore the two sets are equal: \(A=B\).
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
For any two sets, \(A\cap B\subseteq A\cup B\). If the union and intersection are equal, every element in the union must also lie in the intersection. Thus any element belonging to A must belong to B, giving \(A\subseteq B\); similarly, \(B\subseteq A\). Therefore the two sets are equal: \(A=B\).
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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