If A ∪ B = B, which conclusion is necessarily true?
Answer and explanation
Correct answer: A ⊆ B
The equality A ∪ B = B says that adding all elements of A to B does not enlarge B. To prove the result element by element, take any x ∈ A. Then x ∈ A ∪ B, and because the union equals B, x must belong to B. Thus every element of A lies in B, so A ⊆ B. The other options require additional conditions and are not forced by the given equality.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
The equality A ∪ B = B says that adding all elements of A to B does not enlarge B. To prove the result element by element, take any x ∈ A. Then x ∈ A ∪ B, and because the union equals B, x must belong to B. Thus every element of A lies in B, so A ⊆ B. The other options require additional conditions and are not forced by the given equality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
