If A ∪ B = A ∩ B, which conclusion about A and B is correct?
Answer and explanation
Correct answer: A = B
For every pair of sets, A ∩ B is contained in A ∪ B. If the two are equal, then every element that belongs to either set must belong to both sets. Thus every element of A belongs to B, so A ⊆ B; similarly, every element of B belongs to A, so B ⊆ A. Mutual inclusion proves A = B. The other options describe only special cases or contradict the condition.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
For every pair of sets, A ∩ B is contained in A ∪ B. If the two are equal, then every element that belongs to either set must belong to both sets. Thus every element of A belongs to B, so A ⊆ B; similarly, every element of B belongs to A, so B ⊆ A. Mutual inclusion proves A = B. The other options describe only special cases or contradict the condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
