If only n(A−B)=20, n(B−C)=18, and n(C−A)=16 are given, can n(A ∪ B ∪ C) be determined uniquely?
Answer and explanation
Correct answer: No; information about the common regions is needed
The three given differences describe only selected portions of the sets: A outside B, B outside C, and C outside A. They do not determine pairwise-overlap regions, the triple intersection, or other exclusive regions that may contribute to the union. Different Venn diagrams can have the same three difference counts but different union sizes, so the union cannot be determined uniquely.
Frequently asked questions
What is the correct answer to this question?
No; information about the common regions is needed
Why is this the correct answer?
The three given differences describe only selected portions of the sets: A outside B, B outside C, and C outside A. They do not determine pairwise-overlap regions, the triple intersection, or other exclusive regions that may contribute to the union. Different Venn diagrams can have the same three difference counts but different union sizes, so the union cannot be determined uniquely.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
