If \(A\cap B=A\) and \(B\cap C=B\), which conclusion is correct?
Answer and explanation
Correct answer: \(A\subseteq C\)
The equality \(A\cap B=A\) means every element of A is also in B, so \(A\subseteq B\). Similarly, \(B\cap C=B\) means every element of B is in C, so \(B\subseteq C\). Subset inclusion is transitive; therefore \(A\subseteq B\subseteq C\), which gives \(A\subseteq C\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A\subseteq C\)
Why is this the correct answer?
The equality \(A\cap B=A\) means every element of A is also in B, so \(A\subseteq B\). Similarly, \(B\cap C=B\) means every element of B is in C, so \(B\subseteq C\). Subset inclusion is transitive; therefore \(A\subseteq B\subseteq C\), which gives \(A\subseteq C\). Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
