If A ∩ B = B, which of the following relations is true?
Answer and explanation
Correct answer: B ⊆ A
The equality A ∩ B = B means that taking the elements common to A and B leaves all of B unchanged. Therefore every element of B must also belong to A, which is exactly the statement B ⊆ A. A ⊆ B is the reverse implication and is not required. B ⊂ A is too strong because A and B may be equal, and A ∩ B = A would instead imply A ⊆ B.
Frequently asked questions
What is the correct answer to this question?
B ⊆ A
Why is this the correct answer?
The equality A ∩ B = B means that taking the elements common to A and B leaves all of B unchanged. Therefore every element of B must also belong to A, which is exactly the statement B ⊆ A. A ⊆ B is the reverse implication and is not required. B ⊂ A is too strong because A and B may be equal, and A ∩ B = A would instead imply A ⊆ 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).
