In the Venn diagram of A, B, and C, only A ∩ B has 11 elements, only B ∩ C has 13, only C ∩ A has 9, and all three have 4. What is n(A ∩ B) + n(B ∩ C) + n(C ∩ A)?
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Answer and explanation
Correct answer: 45
Each pairwise intersection includes its exclusive pair region as well as the central region common to all three sets. Therefore, n(A ∩ B)=11+4=15, n(B ∩ C)=13+4=17, and n(C ∩ A)=9+4=13. Their sum is 15+17+13=45. The central region is counted three times because it belongs to every pair.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
Each pairwise intersection includes its exclusive pair region as well as the central region common to all three sets. Therefore, n(A ∩ B)=11+4=15, n(B ∩ C)=13+4=17, and n(C ∩ A)=9+4=13. Their sum is 15+17+13=45. The central region is counted three times because it belongs to every pair.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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