In a survey, n(U) = 140, n(A) = 72, n(B) = 64, and n(A ∩ B) = 28. How many people are in neither set?
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Answer and explanation
Correct answer: 32
First find the number in at least one set: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 72 + 64 − 28 = 108. The people in neither set are outside this union but still inside U. Therefore, neither = n(U) − n(A ∪ B) = 140 − 108 = 32. Subtracting the intersection prevents the 28 common people from being counted twice.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
First find the number in at least one set: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 72 + 64 − 28 = 108. The people in neither set are outside this union but still inside U. Therefore, neither = n(U) − n(A ∪ B) = 140 − 108 = 32. Subtracting the intersection prevents the 28 common people from being counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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