If \(A\cap B=A\) and \(A\cup B=B\), which of the following is the correct conclusion?
Answer and explanation
Correct answer: \(A\subseteq B\)
The equality \(A\cap B=A\) means that taking only the elements common to A and B leaves all of A unchanged. Hence every element of A must belong to B, which is exactly \(A\subseteq B\). The second equality, \(A\cup B=B\), expresses the same containment: adding A to B does not introduce any new element. Therefore option A is the necessary conclusion; the other statements do not follow.
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 taking only the elements common to A and B leaves all of A unchanged. Hence every element of A must belong to B, which is exactly \(A\subseteq B\). The second equality, \(A\cup B=B\), expresses the same containment: adding A to B does not introduce any new element. Therefore option A is the necessary conclusion; the other statements do not follow.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
