If A \ B = ∅, which of the following statements must always be true?
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. Therefore every element of A must also be an element of B, which is precisely the definition of A ⊆ B. The condition does not imply that B ⊆ A or that the two sets are complements.
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. Therefore every element of A must also be an element of B, which is precisely the definition of A ⊆ B. The condition does not imply that B ⊆ A or that the two sets are complements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
