If A \ B = B \ A = {2, 5}, what is the correct conclusion?
Answer and explanation
Correct answer: This is impossible
The difference A \ B contains elements that belong to A but not B, whereas B \ A contains elements that belong to B but not A. These two differences are always disjoint. They therefore cannot be equal to the same non-empty set {2, 5}, because that would make 2 and 5 belong to both differences simultaneously. The stated condition is impossible.
Frequently asked questions
What is the correct answer to this question?
This is impossible
Why is this the correct answer?
The difference A \ B contains elements that belong to A but not B, whereas B \ A contains elements that belong to B but not A. These two differences are always disjoint. They therefore cannot be equal to the same non-empty set {2, 5}, because that would make 2 and 5 belong to both differences simultaneously. The stated condition is impossible.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
