In a Venn diagram, why must expressions such as n(A−B)=18, n(B−C)=26, and n(C−A)=21 be handled carefully?
Answer and explanation
Correct answer: Because A−B may include a part of A∩C
In a three-set Venn diagram, A−B means all elements that are in A and not in B. This is not necessarily the same as the region only in A, because some elements may belong to both A and C while still not belonging to B. Thus A−B can contain the only-A region and the A∩C-only region. The same careful interpretation applies to B−C and C−A, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
Because A−B may include a part of A∩C
Why is this the correct answer?
In a three-set Venn diagram, A−B means all elements that are in A and not in B. This is not necessarily the same as the region only in A, because some elements may belong to both A and C while still not belonging to B. Thus A−B can contain the only-A region and the A∩C-only region. The same careful interpretation applies to B−C and C−A, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
