If \(A\setminus B=A\), what conclusion about \(A\) and \(B\) is correct?
Answer and explanation
Correct answer: \(A\cap B=\emptyset\)
The difference \(A\setminus B\) contains the elements of \(A\) that are not in \(B\). If removing the elements of \(B\) from \(A\) leaves all of \(A\) unchanged, then no element of \(A\) can belong to \(B\). Hence the two sets have no common element, so \(A\cap B=\emptyset\). This does not imply that either set is empty or that they are equal; it only establishes that they are disjoint.
Frequently asked questions
What is the correct answer to this question?
\(A\cap B=\emptyset\)
Why is this the correct answer?
The difference \(A\setminus B\) contains the elements of \(A\) that are not in \(B\). If removing the elements of \(B\) from \(A\) leaves all of \(A\) unchanged, then no element of \(A\) can belong to \(B\). Hence the two sets have no common element, so \(A\cap B=\emptyset\). This does not imply that either set is empty or that they are equal; it only establishes that they are disjoint.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
