If \(A\cap B=\varnothing\), then which set is \(A-(A-B)\) equal to?
Answer and explanation
Correct answer: \(\varnothing\)
In general, \(A-(A-B)=A\cap B\). This is because \(A-B\) removes from \(A\) every element that is not in \(B\), leaving only the elements common to both sets. Since the question states that \(A\cap B=\varnothing\), the remaining set is empty. Equivalently, disjointness gives \(A-B=A\), so the expression becomes \(A-A=\varnothing\).
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
In general, \(A-(A-B)=A\cap B\). This is because \(A-B\) removes from \(A\) every element that is not in \(B\), leaving only the elements common to both sets. Since the question states that \(A\cap B=\varnothing\), the remaining set is empty. Equivalently, disjointness gives \(A-B=A\), so the expression becomes \(A-A=\varnothing\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
