In a survey, n(U) = 200 and n(A ∪ B ∪ C) = 164. How many people are in none of the sets?
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Answer and explanation
Correct answer: 36
People in none of the sets are outside the union A ∪ B ∪ C. In set notation, this group is (A ∪ B ∪ C)' within the universal set U. The universal set is divided into the union and its complement, so n(U) = n(A ∪ B ∪ C) + n((A ∪ B ∪ C)'). Therefore, n((A ∪ B ∪ C)') = 200 − 164 = 36. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
People in none of the sets are outside the union A ∪ B ∪ C. In set notation, this group is (A ∪ B ∪ C)' within the universal set U. The universal set is divided into the union and its complement, so n(U) = n(A ∪ B ∪ C) + n((A ∪ B ∪ C)'). Therefore, n((A ∪ B ∪ C)') = 200 − 164 = 36. Hence 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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