If A − B = ∅ and B − A ≠ ∅, which conclusion is correct?
Answer and explanation
Correct answer: A ⊂ B
A − B = ∅ means that no element of A lies outside B; therefore, every element of A belongs to B, so A ⊆ B. The additional condition B − A ≠ ∅ says that at least one element belongs to B but not to A. Hence A is a proper subset of B, written A ⊂ B. Equality and the disjointness condition are therefore impossible.
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; therefore, every element of A belongs to B, so A ⊆ B. The additional condition B − A ≠ ∅ says that at least one element belongs to B but not to A. Hence A is a proper subset of B, written A ⊂ B. Equality and the disjointness condition are therefore 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).
