For three sets, n(A) = 48, n(B) = 50, n(C) = 44, n(A ∩ B) = 20, n(B ∩ C) = 18, n(C ∩ A) = 16, and n(A ∩ B ∩ C) = 7. What is n(A ∪ B ∪ C)?
Answer and explanation
Correct answer: 95
Use the three-set inclusion–exclusion formula: 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 48 + 50 + 44 − 20 − 18 − 16 + 7 = 95. The pairwise intersections are subtracted to remove duplicate counting, while the central triple intersection is added once because it was subtracted too many times.
Frequently asked questions
What is the correct answer to this question?
95
Why is this the correct answer?
Use the three-set inclusion–exclusion formula: 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 48 + 50 + 44 − 20 − 18 − 16 + 7 = 95. The pairwise intersections are subtracted to remove duplicate counting, while the central triple intersection is added once because it was subtracted too many times.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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