If A ∪ B = A △ B, where A △ B = (A \ B) ∪ (B \ A), which conclusion must be true?
Answer and explanation
Correct answer: A ∩ B = ∅
The union A ∪ B contains elements in A, in B, and also elements common to both sets. The symmetric difference A △ B contains only elements belonging to exactly one of the two sets; it excludes A ∩ B. Therefore the two sets can be equal only when there are no common elements. Hence A ∩ B = ∅, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅
Why is this the correct answer?
The union A ∪ B contains elements in A, in B, and also elements common to both sets. The symmetric difference A △ B contains only elements belonging to exactly one of the two sets; it excludes A ∩ B. Therefore the two sets can be equal only when there are no common elements. Hence A ∩ B = ∅, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
