If \(A\cap B=A\), which conclusion is correct?
Answer and explanation
Correct answer: \(A\subseteq B\)
The equality \(A\cap B=A\) means that intersecting A with B removes nothing from A. Consequently, every element of A must already be in B, so \(A\subseteq B\). The reverse relation \(B\subseteq A\) is not required; for example, A may be a proper subset of B. The complement and empty-union statements also do not follow. Therefore option A is the uniquely necessary conclusion.
Frequently asked questions
What is the correct answer to this question?
\(A\subseteq B\)
Why is this the correct answer?
The equality \(A\cap B=A\) means that intersecting A with B removes nothing from A. Consequently, every element of A must already be in B, so \(A\subseteq B\). The reverse relation \(B\subseteq A\) is not required; for example, A may be a proper subset of B. The complement and empty-union statements also do not follow. Therefore option A is the uniquely necessary conclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
