If n(A ∪ B ∪ C) = 160, n(A) = 70, n(B) = 75, n(C) = 80 and n(A ∩ B ∩ C) = 18, then what is n(A ∩ B) + n(B ∩ C) + n(C ∩ A)?
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Answer and explanation
Correct answer: 83
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). Substituting the given values gives 160 = 70 + 75 + 80 − S + 18, where S is the required pairwise-intersection sum. Thus 160 = 243 − S, so S = 83.
Frequently asked questions
What is the correct answer to this question?
83
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). Substituting the given values gives 160 = 70 + 75 + 80 − S + 18, where S is the required pairwise-intersection sum. Thus 160 = 243 − S, so S = 83.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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