For three sets A, B, C, n(A∩B)=21, n(B∩C)=19, n(C∩A)=16, and n(A∩B∩C)=7. How many elements belong to exactly two of the sets?
Answer and explanation
Correct answer: 35
Each pairwise intersection includes the seven elements common to all three sets. Therefore, the regions belonging to exactly two sets are (21−7), (19−7), and (16−7). Their total is 14+12+9=35. The triple intersection must be subtracted separately from each pairwise intersection because it is included in all three given pair counts.
Frequently asked questions
What is the correct answer to this question?
35
Why is this the correct answer?
Each pairwise intersection includes the seven elements common to all three sets. Therefore, the regions belonging to exactly two sets are (21−7), (19−7), and (16−7). Their total is 14+12+9=35. The triple intersection must be subtracted separately from each pairwise intersection because it is included in all three given pair counts.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
