If n(A − B) = 18, n(B − C) = 25, and n(C − A) = 20, can n(A ∪ B ∪ C) be determined uniquely from only these data?
Answer and explanation
Correct answer: No, information about common regions is needed
The values n(A − B), n(B − C), and n(C − A) describe only selected portions of the three sets. They do not reveal the sizes of regions shared by two sets or by all three sets, and those regions contribute to the union. Different Venn diagrams can therefore have the same three given differences but different union sizes. Additional common-region information is necessary.
Frequently asked questions
What is the correct answer to this question?
No, information about common regions is needed
Why is this the correct answer?
The values n(A − B), n(B − C), and n(C − A) describe only selected portions of the three sets. They do not reveal the sizes of regions shared by two sets or by all three sets, and those regions contribute to the union. Different Venn diagrams can therefore have the same three given differences but different union sizes. Additional common-region information is necessary.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
