If \(A\cap B=B\), which conclusion is correct?
Answer and explanation
Correct answer: \(B\subseteq A\)
The intersection \(A\cap B\) contains elements common to both sets. If this intersection is exactly \(B\), then every element of \(B\) must also belong to \(A\). Therefore, \(B\) is a subset of \(A\), written as \(B\subseteq A\). The statement does not necessarily imply that every element of \(A\) belongs to \(B\), so \(A\subseteq B\) is not required.
Frequently asked questions
What is the correct answer to this question?
\(B\subseteq A\)
Why is this the correct answer?
The intersection \(A\cap B\) contains elements common to both sets. If this intersection is exactly \(B\), then every element of \(B\) must also belong to \(A\). Therefore, \(B\) is a subset of \(A\), written as \(B\subseteq A\). The statement does not necessarily imply that every element of \(A\) belongs to \(B\), so \(A\subseteq B\) is not required.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
