If n(A) = 8, n(B) = 7, n(C) = 6, n(A ∩ B) = 2, n(A ∩ C) = 1, n(B ∩ C) = 3, and n(A ∩ B ∩ C) = 1, what is n(A ∪ B ∪ C)?
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Answer and explanation
Correct answer: 16
Use the three-set inclusion–exclusion formula: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C). Substitution gives 8 + 7 + 6 − 2 − 1 − 3 + 1 = 16. The triple intersection is added once because it was over-subtracted.
Frequently asked questions
What is the correct answer to this question?
16
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(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C). Substitution gives 8 + 7 + 6 − 2 − 1 − 3 + 1 = 16. The triple intersection is added once because it was over-subtracted.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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