If n(A) = 35, n(B) = 30, and n(A ∪ B) = 50, what is n(A ∩ B) in the Venn diagram?
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Answer and explanation
Correct answer: 15
Use the inclusion-exclusion identity for two sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Therefore, n(A ∩ B) = 35 + 30 − 50 = 15. The intersection is the part counted in both sets, so it is the amount that must be removed from the sum of the two separate set sizes to obtain the union.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
Use the inclusion-exclusion identity for two sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Therefore, n(A ∩ B) = 35 + 30 − 50 = 15. The intersection is the part counted in both sets, so it is the amount that must be removed from the sum of the two separate set sizes to obtain the union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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