If \(A\cap B=B\), which of the following statements is true?
Answer and explanation
Correct answer: \(B\subseteq A\)
The equality \(A\cap B=B\) means that intersecting \(B\) with \(A\) does not remove any element from \(B\). Therefore, every element of \(B\) must already belong to \(A\), which gives \(B\subseteq A\). The reverse relation \(A\subseteq B\) does not necessarily hold, because \(A\) may contain additional elements. The complement statement is unrelated, and the intersection cannot be empty unless \(B\) is empty.
Frequently asked questions
What is the correct answer to this question?
\(B\subseteq A\)
Why is this the correct answer?
The equality \(A\cap B=B\) means that intersecting \(B\) with \(A\) does not remove any element from \(B\). Therefore, every element of \(B\) must already belong to \(A\), which gives \(B\subseteq A\). The reverse relation \(A\subseteq B\) does not necessarily hold, because \(A\) may contain additional elements. The complement statement is unrelated, and the intersection cannot be empty unless \(B\) is empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
