If n(A ∩ Bᶜ) = 52, n(Aᶜ ∩ B) = 39, and n(A △ B) = 100, what is the correct conclusion about the data?
Answer and explanation
Correct answer: The data are inconsistent
The symmetric difference is defined as A △ B = (A ∩ Bᶜ) ∪ (Aᶜ ∩ B). These two regions are disjoint, so their cardinalities must be added: n(A △ B) = 52 + 39 = 91. Since the question states that n(A △ B) is 100, the two pieces contradict the stated symmetric difference. Therefore, the data are inconsistent. The intersection A ∩ B is not included in the symmetric difference.
Frequently asked questions
What is the correct answer to this question?
The data are inconsistent
Why is this the correct answer?
The symmetric difference is defined as A △ B = (A ∩ Bᶜ) ∪ (Aᶜ ∩ B). These two regions are disjoint, so their cardinalities must be added: n(A △ B) = 52 + 39 = 91. Since the question states that n(A △ B) is 100, the two pieces contradict the stated symmetric difference. Therefore, the data are inconsistent. The intersection A ∩ B is not included in the symmetric difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
