If A ∪ B = A and B ∪ C = C, which relation must be true?
Answer and explanation
Correct answer: B ⊆ A ∩ C
The equality A ∪ B = A means that every element of B is already in A; otherwise the union would contain an additional element. Thus B ⊆ A. Similarly, B ∪ C = C means that every element of B is already in C, so B ⊆ C. Being a subset of both A and C means being a subset of their intersection. Therefore B ⊆ A ∩ C, making option A correct.
Frequently asked questions
What is the correct answer to this question?
B ⊆ A ∩ C
Why is this the correct answer?
The equality A ∪ B = A means that every element of B is already in A; otherwise the union would contain an additional element. Thus B ⊆ A. Similarly, B ∪ C = C means that every element of B is already in C, so B ⊆ C. Being a subset of both A and C means being a subset of their intersection. Therefore B ⊆ A ∩ C, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
