If A, B and C are mutually disjoint, n(A) = 18, n(B) = 24, n(C) = 29 and n(U) = 90, then what is n((A ∪ B ∪ C)')?
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Answer and explanation
Correct answer: 19
Because A, B and C are mutually disjoint, no element belongs to more than one of these sets. Thus, the size of their union is the sum of their individual sizes: n(A ∪ B ∪ C) = 18 + 24 + 29 = 71. The complement contains all elements of the universal set that are outside this union. Therefore, n((A ∪ B ∪ C)') = 90 − 71 = 19.
Frequently asked questions
What is the correct answer to this question?
19
Why is this the correct answer?
Because A, B and C are mutually disjoint, no element belongs to more than one of these sets. Thus, the size of their union is the sum of their individual sizes: n(A ∪ B ∪ C) = 18 + 24 + 29 = 71. The complement contains all elements of the universal set that are outside this union. Therefore, n((A ∪ B ∪ C)') = 90 − 71 = 19.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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