If A \ B = B \ A, which conclusion is correct?
Answer and explanation
Correct answer: A = B
The sets A \ B and B \ A represent the elements belonging exclusively to A and exclusively to B, respectively. They are always disjoint. If two disjoint sets are equal, their common value must be empty; hence A \ B = ∅ and B \ A = ∅. Therefore A has no element outside B and B has no element outside A, so A = B.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The sets A \ B and B \ A represent the elements belonging exclusively to A and exclusively to B, respectively. They are always disjoint. If two disjoint sets are equal, their common value must be empty; hence A \ B = ∅ and B \ A = ∅. Therefore A has no element outside B and B has no element outside A, so A = B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
