If n(A ∪ B) = 36, the A-only region has 14 elements, and the B-only region has 11 elements, what is n(A ∩ B)?
Answer and explanation
Correct answer: 11
The union A ∪ B is made up of three mutually disjoint parts: the A-only region, the common region A ∩ B, and the B-only region. Therefore, its cardinality is the sum of these three parts: 36 = 14 + n(A ∩ B) + 11. Rearranging gives n(A ∩ B) = 36 − 14 − 11 = 11. Hence, option B is correct; 14 and 11 are already given region counts, while 25 is their sum.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The union A ∪ B is made up of three mutually disjoint parts: the A-only region, the common region A ∩ B, and the B-only region. Therefore, its cardinality is the sum of these three parts: 36 = 14 + n(A ∩ B) + 11. Rearranging gives n(A ∩ B) = 36 − 14 − 11 = 11. Hence, option B is correct; 14 and 11 are already given region counts, while 25 is their sum.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
