If A \ B = ∅ and B \ A = ∅, which conclusion is correct?
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Answer and explanation
Correct answer: A = B
A \ B = ∅ means that no element of A lies outside B, so every element of A belongs to B; hence A ⊆ B. Similarly, B \ A = ∅ gives B ⊆ A. Since each set is contained in the other, the two sets have exactly the same elements, and therefore A = B. The other conclusions do not follow.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
A \ B = ∅ means that no element of A lies outside B, so every element of A belongs to B; hence A ⊆ B. Similarly, B \ A = ∅ gives B ⊆ A. Since each set is contained in the other, the two sets have exactly the same elements, and therefore A = B. The other conclusions do not follow.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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