If n(U) = 80, the number of elements outside both sets is 15, only A has 25 elements, and only B has 18 elements, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 22
A two-set Venn diagram partitions U into four disjoint regions: outside both sets, only A, only B, and A ∩ B. Let the unknown intersection size be x. Then 15 + 25 + 18 + x = 80, so x = 80 − 58 = 22. Therefore n(A ∩ B) = 22. The other choices result from omitting or combining one or more regions incorrectly.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
A two-set Venn diagram partitions U into four disjoint regions: outside both sets, only A, only B, and A ∩ B. Let the unknown intersection size be x. Then 15 + 25 + 18 + x = 80, so x = 80 − 58 = 22. Therefore n(A ∩ B) = 22. The other choices result from omitting or combining one or more regions incorrectly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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