For three sets, n(A) = 72, n(B) = 66, n(C) = 59, n(A ∩ B) = 28, n(B ∩ C) = 24, n(C ∩ A) = 22, and n(A ∩ B ∩ C) = 9. What is n(A ∪ B ∪ C)?
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Answer and explanation
Correct answer: 132
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 72 + 66 + 59 − 28 − 24 − 22 + 9 = 132. The triple intersection is added once because it was subtracted too many times during the pairwise correction.
Frequently asked questions
What is the correct answer to this question?
132
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 72 + 66 + 59 − 28 − 24 − 22 + 9 = 132. The triple intersection is added once because it was subtracted too many times during the pairwise correction.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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