For three sets, n(A∩B)=18, n(B∩C)=16, n(C∩A)=14, and n(A∩B∩C)=6. How many elements belong to exactly two of the sets?
Answer and explanation
Correct answer: 30
For each pairwise intersection, remove the elements that are also in the third set. Thus, elements only in A and B are 18−6=12, only in B and C are 16−6=10, and only in C and A are 14−6=8. These three disjoint regions contain exactly two-set members, so the total is 12+10+8=30. The triple intersection must be removed from every pair.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
For each pairwise intersection, remove the elements that are also in the third set. Thus, elements only in A and B are 18−6=12, only in B and C are 16−6=10, and only in C and A are 14−6=8. These three disjoint regions contain exactly two-set members, so the total is 12+10+8=30. The triple intersection must be removed from every pair.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
