If \(A\subseteq B\), what is \(A\setminus B\) equal to?
Answer and explanation
Correct answer: \(\emptyset\)
The difference \(A\setminus B\) consists of elements that belong to \(A\) but do not belong to \(B\). Since \(A\subseteq B\), every element of \(A\) is already in \(B\). Consequently, there is no element of \(A\) outside \(B\), so the difference contains no elements and equals \(\emptyset\). For example, if \(A=\{1,2\}\) and \(B=\{1,2,3\}\), then removing all elements of \(B\) from \(A\) leaves nothing.
Frequently asked questions
What is the correct answer to this question?
\(\emptyset\)
Why is this the correct answer?
The difference \(A\setminus B\) consists of elements that belong to \(A\) but do not belong to \(B\). Since \(A\subseteq B\), every element of \(A\) is already in \(B\). Consequently, there is no element of \(A\) outside \(B\), so the difference contains no elements and equals \(\emptyset\). For example, if \(A=\{1,2\}\) and \(B=\{1,2,3\}\), then removing all elements of \(B\) from \(A\) leaves nothing.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
