If A ⊆ B, which of the following statements is always true?
Answer and explanation
Correct answer: A ∪ B = B
The relation A ⊆ B means that every element of A is already an element of B. Therefore, taking the union of A and B adds no new element to B, so A ∪ B = B. Also, A ∩ B = A and A \ B = ∅. Option B would require B ⊆ A, while option C would also require B ⊆ A. Option D is not generally possible because A \ B is empty, not equal to B.
Frequently asked questions
What is the correct answer to this question?
A ∪ B = B
Why is this the correct answer?
The relation A ⊆ B means that every element of A is already an element of B. Therefore, taking the union of A and B adds no new element to B, so A ∪ B = B. Also, A ∩ B = A and A \ B = ∅. Option B would require B ⊆ A, while option C would also require B ⊆ A. Option D is not generally possible because A \ B is empty, not equal to 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).
