If \(A\subseteq B\) and \(B\subseteq C\), what is \(A\cap C\) equal to?
Answer and explanation
Correct answer: \(A\)
Because subset inclusion is transitive, \(A\subseteq B\) and \(B\subseteq C\) imply \(A\subseteq C\). When one set is a subset of another, their intersection is the smaller set: if \(X\subseteq Y\), then \(X\cap Y=X\). Therefore, \(A\cap C=A\). The other choices are not generally correct: \(B\) and \(C\) may contain additional elements, while the empty set would occur only if \(A\) itself were empty.
Frequently asked questions
What is the correct answer to this question?
\(A\)
Why is this the correct answer?
Because subset inclusion is transitive, \(A\subseteq B\) and \(B\subseteq C\) imply \(A\subseteq C\). When one set is a subset of another, their intersection is the smaller set: if \(X\subseteq Y\), then \(X\cap Y=X\). Therefore, \(A\cap C=A\). The other choices are not generally correct: \(B\) and \(C\) may contain additional elements, while the empty set would occur only if \(A\) itself were empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
