In a Venn diagram, n(U) = 110, n(A) = 57, n(B) = 49, and n(A ∩ B) = 21. What is n(A ∪ B)?
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Answer and explanation
Correct answer: 85
For two finite sets, the cardinality of the union is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The common 21 elements are present in both A and B, so they would be counted twice in 57 + 49 and must be subtracted once. Therefore, n(A ∪ B) = 57 + 49 − 21 = 85. The value of n(U) is not needed for this calculation.
Frequently asked questions
What is the correct answer to this question?
85
Why is this the correct answer?
For two finite sets, the cardinality of the union is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The common 21 elements are present in both A and B, so they would be counted twice in 57 + 49 and must be subtracted once. Therefore, n(A ∪ B) = 57 + 49 − 21 = 85. The value of n(U) is not needed for this calculation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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