In a survey, the universal set U has 200 people, and 164 people belong to at least one of the sets A, B, or C. How many people belong to none of the three sets?
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Answer and explanation
Correct answer: 36
The union A ∪ B ∪ C represents everyone who belongs to at least one of the three sets. The people in none of the sets are outside this union, so their number is found by subtracting the union from the universal set: n(U) − n(A ∪ B ∪ C) = 200 − 164 = 36. Therefore, 36 people belong to none of the three sets.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
The union A ∪ B ∪ C represents everyone who belongs to at least one of the three sets. The people in none of the sets are outside this union, so their number is found by subtracting the union from the universal set: n(U) − n(A ∪ B ∪ C) = 200 − 164 = 36. Therefore, 36 people belong to none of the three sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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