Which option is always true?
Answer and explanation
Correct answer: \(A\cap B\subseteq A\)
The intersection \(A\cap B\) is defined as the set of elements that belong to both \(A\) and \(B\). Since every element in the intersection necessarily belongs to \(A\), it follows that \(A\cap B\subseteq A\) for all sets \(A\) and \(B\). The other statements are not universally true: the two differences may differ, equality of union and intersection is exceptional, and \(A\subseteq A-B\) generally fails when the sets overlap.
Frequently asked questions
What is the correct answer to this question?
\(A\cap B\subseteq A\)
Why is this the correct answer?
The intersection \(A\cap B\) is defined as the set of elements that belong to both \(A\) and \(B\). Since every element in the intersection necessarily belongs to \(A\), it follows that \(A\cap B\subseteq A\) for all sets \(A\) and \(B\). The other statements are not universally true: the two differences may differ, equality of union and intersection is exceptional, and \(A\subseteq A-B\) generally fails when the sets overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
