For three sets, n(A)=64, n(B)=58, n(C)=52, n(A∩B)=24, n(B∩C)=21, n(C∩A)=19, and n(A∩B∩C)=8. What is n(A∪B∪C)?
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Answer and explanation
Correct answer: 118
Apply 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 64+58+52−24−21−19+8=118. The pairwise intersections are subtracted because they were counted twice, while the triple intersection is added once because it was then subtracted too many times.
Frequently asked questions
What is the correct answer to this question?
118
Why is this the correct answer?
Apply 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 64+58+52−24−21−19+8=118. The pairwise intersections are subtracted because they were counted twice, while the triple intersection is added once because it was then 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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