If A − B = ∅, which conclusion is correct?
Answer and explanation
Correct answer: A ⊆ B
The difference A − B consists of elements that belong to A but do not belong to B. If this difference is empty, there is no element of A outside B. Consequently, every element of A must also belong to B, which is exactly the statement A ⊆ B. Equality is not implied because B may contain additional elements. The reverse subset relation and disjointness are also not guaranteed.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
The difference A − B consists of elements that belong to A but do not belong to B. If this difference is empty, there is no element of A outside B. Consequently, every element of A must also belong to B, which is exactly the statement A ⊆ B. Equality is not implied because B may contain additional elements. The reverse subset relation and disjointness are also not guaranteed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
