If \(A=\{1,2,3,4\}\) and \(B=\{2,3\}\), which statement about \(A-B\) is correct?
Answer and explanation
Correct answer: \(A-B=\{1,4\}\) and it is a subset of \(A\)
The difference \(A-B\) consists of all elements that belong to \(A\) but do not belong to \(B\). From \(A=\{1,2,3,4\}\), remove 2 and 3 because both are in \(B\). The remaining elements are 1 and 4, so \(A-B=\{1,4\}\). Every element of this difference already belongs to \(A\), so it is a subset of \(A\). Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A-B=\{1,4\}\) and it is a subset of \(A\)
Why is this the correct answer?
The difference \(A-B\) consists of all elements that belong to \(A\) but do not belong to \(B\). From \(A=\{1,2,3,4\}\), remove 2 and 3 because both are in \(B\). The remaining elements are 1 and 4, so \(A-B=\{1,4\}\). Every element of this difference already belongs to \(A\), so it is a subset of \(A\). Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
