If A and B are finite sets and n(A ∪ B) = n(A) + n(B), which conclusion is correct?
Answer and explanation
Correct answer: A ∩ B = ∅
For two finite sets, the inclusion-exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The given equality has no subtraction term, so n(A ∩ B) must be zero. A finite set with zero elements is empty; therefore A ∩ B = ∅. This means A and B are disjoint, but it does not imply equality or either subset relation. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅
Why is this the correct answer?
For two finite sets, the inclusion-exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The given equality has no subtraction term, so n(A ∩ B) must be zero. A finite set with zero elements is empty; therefore A ∩ B = ∅. This means A and B are disjoint, but it does not imply equality or either subset relation. Hence option A is 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).
