If n(A)=30, n(B)=28, n(C)=24, n(A ∩ B)=10, n(B ∩ C)=8, n(C ∩ A)=6, and n(A ∩ B ∩ C)=4, what is n(A ∪ B ∪ C)?
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Answer and explanation
Correct answer: 62
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 30+28+24−10−8−6+4=62. The triple intersection is added once because it was subtracted twice while removing the pairwise overlaps.
Frequently asked questions
What is the correct answer to this question?
62
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 30+28+24−10−8−6+4=62. The triple intersection is added once because it was subtracted twice while removing the pairwise overlaps.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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