If n(A) = 40, n(B) = 36, n(C) = 28, n(A ∩ B) = 14, n(B ∩ C) = 10, n(C ∩ A) = 12, and n(A ∩ B ∩ C) = 5, then what is n((A ∪ B ∪ C) − C)?
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Answer and explanation
Correct answer: 45
First apply the inclusion–exclusion formula: n(A ∪ B ∪ C) = 40 + 36 + 28 − 14 − 10 − 12 + 5 = 73. Since C is contained in the union, removing C removes exactly 28 elements. Therefore n((A ∪ B ∪ C) − C) = 73 − 28 = 45. The triple intersection has already been handled correctly by inclusion–exclusion.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
First apply the inclusion–exclusion formula: n(A ∪ B ∪ C) = 40 + 36 + 28 − 14 − 10 − 12 + 5 = 73. Since C is contained in the union, removing C removes exactly 28 elements. Therefore n((A ∪ B ∪ C) − C) = 73 − 28 = 45. The triple intersection has already been handled correctly by inclusion–exclusion.
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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