If \(A\cap B=A\cup B\), what is the correct statement about A and B?
Answer and explanation
Correct answer: \(A=B\)
For any two sets, \(A\cap B\subseteq A\cup B\) always holds. Equality can occur only when no element belongs to one set without also belonging to the other. Equivalently, every element of A is in B and every element of B is in A. Hence both mutual containments hold, which proves \(A=B\). The condition does not require the sets to be empty.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
For any two sets, \(A\cap B\subseteq A\cup B\) always holds. Equality can occur only when no element belongs to one set without also belonging to the other. Equivalently, every element of A is in B and every element of B is in A. Hence both mutual containments hold, which proves \(A=B\). The condition does not require the sets to be 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).
