If A ∪ B = A and A ∩ B = B, which relation is correct?
Answer and explanation
Correct answer: B ⊆ A
The equality A ∪ B = A means that adding B to A introduces no new elements. Consequently, every element of B must already belong to A, which is precisely B ⊆ A. The second condition, A ∩ B = B, gives the same conclusion because every element of B is common to A and B. The sets need not be equal or empty, so option A is the only valid relation.
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 B to A introduces no new elements. Consequently, every element of B must already belong to A, which is precisely B ⊆ A. The second condition, A ∩ B = B, gives the same conclusion because every element of B is common to A and B. The sets need not be equal or empty, so option A is the only valid relation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
