If only n(A−B)=24, n(B−C)=27 and n(C−A)=22 are given, can n(A∪B∪C) be determined uniquely?
Answer and explanation
Correct answer: No, information about common regions is needed
Each difference includes more than one possible Venn region; for example, A−B may contain the part only in A and the part in A∩C but not B. The three given counts therefore do not specify all single, pairwise, and triple regions. Different common-region counts can produce different unions, so the union cannot be determined uniquely.
Frequently asked questions
What is the correct answer to this question?
No, information about common regions is needed
Why is this the correct answer?
Each difference includes more than one possible Venn region; for example, A−B may contain the part only in A and the part in A∩C but not B. The three given counts therefore do not specify all single, pairwise, and triple regions. Different common-region counts can produce different unions, 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: Venn Diagrams.
