If n(A − B) = 27, n(B − C) = 31, n(C − A) = 24, and the three sets are drawn generally, why is n(A ∪ B ∪ C) not determined from these alone?
Answer and explanation
Correct answer: Because several inner regions are still unknown
The quantities n(A − B), n(B − C), and n(C − A) describe only selected portions of a three-set Venn diagram. They do not tell us the sizes of several other regions, such as the pairwise-overlap parts, the central triple intersection, or possibly other exclusive regions. Since the union is the sum of every region inside at least one circle, different diagrams can satisfy the given values but have different union sizes. Therefore, the union cannot be determined from these data alone.
Frequently asked questions
What is the correct answer to this question?
Because several inner regions are still unknown
Why is this the correct answer?
The quantities n(A − B), n(B − C), and n(C − A) describe only selected portions of a three-set Venn diagram. They do not tell us the sizes of several other regions, such as the pairwise-overlap parts, the central triple intersection, or possibly other exclusive regions. Since the union is the sum of every region inside at least one circle, different diagrams can satisfy the given values but have different union sizes. Therefore, the union cannot be determined from these data alone.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
