If A △ B = ∅, which conclusion is correct?
Answer and explanation
Correct answer: A = B
The symmetric difference A △ B contains elements that belong to exactly one of the two sets: elements of A not in B together with elements of B not in A. If this set is empty, neither set has an element absent from the other. Therefore A ⊆ B and B ⊆ A simultaneously, which proves A = B. A proper-subset relation would require one set to have an extra element, and disjointness is not implied.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The symmetric difference A △ B contains elements that belong to exactly one of the two sets: elements of A not in B together with elements of B not in A. If this set is empty, neither set has an element absent from the other. Therefore A ⊆ B and B ⊆ A simultaneously, which proves A = B. A proper-subset relation would require one set to have an extra element, and disjointness is not implied.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
