If \(A\) and \(B\) are sets such that \(A\cap B=\varnothing\), what is the value of \((A\cup B)\setminus B\)?
Answer and explanation
Correct answer: \(A\)
The condition \(A\cap B=\varnothing\) means that A and B have no common elements. The union \(A\cup B\) contains every element of both sets. When all elements belonging to B are removed from this union, no element of A is removed because A and B are disjoint. Therefore, only A remains, so \((A\cup B)\setminus B=A\). This also follows from the identity \((A\cup B)\setminus B=A\setminus B\), together with \(A\setminus B=A\) for disjoint sets.
Frequently asked questions
What is the correct answer to this question?
\(A\)
Why is this the correct answer?
The condition \(A\cap B=\varnothing\) means that A and B have no common elements. The union \(A\cup B\) contains every element of both sets. When all elements belonging to B are removed from this union, no element of A is removed because A and B are disjoint. Therefore, only A remains, so \((A\cup B)\setminus B=A\). This also follows from the identity \((A\cup B)\setminus B=A\setminus B\), together with \(A\setminus B=A\) for disjoint sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
