For three sets, n(A)=35, n(B)=32, n(C)=29, n(A∩B)=12, n(B∩C)=10, n(C∩A)=9, and n(A∩B∩C)=4. What is n(A∪B∪C)?
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Answer and explanation
Correct answer: 69
Use the inclusion–exclusion formula for three sets: n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C). Substitution gives 35+32+29−12−10−9+4=69. Pairwise overlaps are subtracted because they were counted twice, while the triple overlap is added once because it was subtracted too many times.
Frequently asked questions
What is the correct answer to this question?
69
Why is this the correct answer?
Use the inclusion–exclusion formula for three sets: n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C). Substitution gives 35+32+29−12−10−9+4=69. Pairwise overlaps are subtracted because they were counted twice, while the triple overlap is added once because it was subtracted too many times.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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