If A ∪ B = A, which statement is definitely true?
Answer and explanation
Correct answer: B ⊆ A
The equality A ∪ B = A means that adding every element of B to A produces no new element. Therefore, every element already in B must also belong to A. This is precisely the definition of B ⊆ A. The other statements are not necessary: A and B may overlap, neither set must be empty, and A need not be a subset of B.
Frequently asked questions
What is the correct answer to this question?
B ⊆ A
Why is this the correct answer?
The equality A ∪ B = A means that adding every element of B to A produces no new element. Therefore, every element already in B must also belong to A. This is precisely the definition of B ⊆ A. The other statements are not necessary: A and B may overlap, neither set must be empty, and A need not be a subset of B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
