Which option is equal to \((A\cup B)-A\)?
Answer and explanation
Correct answer: \(B-A\)
The union \(A\cup B\) contains every element of A and every element of B. When A is removed from this union, all elements belonging to A disappear, including those that may also be in B. The elements left are precisely the elements that belong to B but do not belong to A. Therefore, \((A\cup B)-A=B-A\), so option A is correct. This is a standard identity involving union and set difference.
Frequently asked questions
What is the correct answer to this question?
\(B-A\)
Why is this the correct answer?
The union \(A\cup B\) contains every element of A and every element of B. When A is removed from this union, all elements belonging to A disappear, including those that may also be in B. The elements left are precisely the elements that belong to B but do not belong to A. Therefore, \((A\cup B)-A=B-A\), so option A is correct. This is a standard identity involving union and set difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
