In three sets, only A = 31, only B = 26, only C = 24, only A ∩ B = 15, only B ∩ C = 13, only C ∩ A = 11, and A ∩ B ∩ C = 8. If n(U) = 160, what is n((A ∪ B ∪ C)ᶜ)?
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Answer and explanation
Correct answer: 32
The seven listed regions are mutually disjoint and together form A ∪ B ∪ C. Their total is 31 + 26 + 24 + 15 + 13 + 11 + 8 = 128. The complement contains all universal-set elements outside the union, so n((A ∪ B ∪ C)ᶜ) = n(U) − n(A ∪ B ∪ C) = 160 − 128 = 32. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The seven listed regions are mutually disjoint and together form A ∪ B ∪ C. Their total is 31 + 26 + 24 + 15 + 13 + 11 + 8 = 128. The complement contains all universal-set elements outside the union, so n((A ∪ B ∪ C)ᶜ) = n(U) − n(A ∪ B ∪ C) = 160 − 128 = 32. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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