If n(A) = 16, n(B) = 18, n(C) = 9, n(A ∩ B) = 6, n(A ∩ C) = 2, n(B ∩ C) = 3, and n(A ∩ B ∩ C) = 1, what is n(A ∪ B ∪ C)?
Answer and explanation
Correct answer: 33
For three finite sets, the inclusion–exclusion formula is n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C). Substituting the values gives 16 + 18 + 9 − 6 − 2 − 3 + 1 = 33. The pairwise intersections are subtracted because they were counted twice, while the triple intersection is added once because it was subtracted too many times.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
For three finite sets, the inclusion–exclusion formula is n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C). Substituting the values gives 16 + 18 + 9 − 6 − 2 − 3 + 1 = 33. The pairwise intersections are subtracted because they were counted twice, while 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.
