In a class, n(U) = 90, n(A) = 52, n(B) = 47, and n(A ∩ B) = 24. How many students are in neither A nor B?
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Answer and explanation
Correct answer: 15
First find the number in at least one of the two sets using inclusion-exclusion: n(A ∪ B) = 52 + 47 − 24 = 75. Students in neither set are outside this union, so their number is n(U) − n(A ∪ B) = 90 − 75 = 15. Equivalently, this is n((A ∪ B)ᶜ). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
First find the number in at least one of the two sets using inclusion-exclusion: n(A ∪ B) = 52 + 47 − 24 = 75. Students in neither set are outside this union, so their number is n(U) − n(A ∪ B) = 90 − 75 = 15. Equivalently, this is n((A ∪ B)ᶜ). 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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