If \(A\setminus B=\varnothing\) and \(B\setminus A=\varnothing\), which conclusion is correct?
Answer and explanation
Correct answer: \(A=B\)
The statement \(A\setminus B=\varnothing\) means that A has no element outside B, so \(A\subseteq B\). Similarly, \(B\setminus A=\varnothing\) implies \(B\subseteq A\). Since each set is a subset of the other, the two sets have exactly the same elements. Therefore, \(A=B\). The conditions do not imply that the sets are empty or disjoint.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The statement \(A\setminus B=\varnothing\) means that A has no element outside B, so \(A\subseteq B\). Similarly, \(B\setminus A=\varnothing\) implies \(B\subseteq A\). Since each set is a subset of the other, the two sets have exactly the same elements. Therefore, \(A=B\). The conditions do not imply that the sets are empty or disjoint.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
