If \(A-B=A\), which statement is correct?
Answer and explanation
Correct answer: \(A\cap B=\varnothing\)
The difference \(A-B\) removes from A every element that also belongs to B. If the result is still exactly A, no element of A can have been removed. Therefore A and B have no common element, which means \(A\cap B=\varnothing\). Notice that B may contain elements outside A; it need not itself be empty.
Frequently asked questions
What is the correct answer to this question?
\(A\cap B=\varnothing\)
Why is this the correct answer?
The difference \(A-B\) removes from A every element that also belongs to B. If the result is still exactly A, no element of A can have been removed. Therefore A and B have no common element, which means \(A\cap B=\varnothing\). Notice that B may contain elements outside A; it need not itself be empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
