For three sets, n(A) = 40, n(B) = 38, n(C) = 35, n(A ∩ B) = 14, n(B ∩ C) = 12, n(C ∩ A) = 10, and n(A ∩ B ∩ C) = 5. What is n(A ∪ B ∪ C)?
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Answer and explanation
Correct answer: 82
For three sets, inclusion-exclusion gives 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 40 + 38 + 35 − 14 − 12 − 10 + 5 = 82. The triple intersection is added once because it was subtracted too many times.
Frequently asked questions
What is the correct answer to this question?
82
Why is this the correct answer?
For three sets, inclusion-exclusion gives 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 40 + 38 + 35 − 14 − 12 − 10 + 5 = 82. The triple intersection 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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