In a class, n(U) = 50, n(A) = 28, n(B) = 22, and n(A ∩ B) = 10. What is n(A ∪ B)?
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Answer and explanation
Correct answer: 40
For two finite sets, the union formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 28 + 22 − 10 = 40. The intersection is subtracted once because its elements were counted in both n(A) and n(B). Thus, the number of students in at least one of the two sets is 40.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
For two finite sets, the union formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 28 + 22 − 10 = 40. The intersection is subtracted once because its elements were counted in both n(A) and n(B). Thus, the number of students in at least one of the two sets is 40.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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