If n(U) = 45 and n(A ∪ B) = 29, how many elements are in the region belonging to neither A nor B in the Venn diagram?
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Answer and explanation
Correct answer: 16
The region that belongs to neither A nor B is the complement of their union, written as (A ∪ B)′. Since the universal set U contains 45 elements and the union contains 29 elements, the elements outside both sets are n((A ∪ B)′) = n(U) − n(A ∪ B) = 45 − 29 = 16. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The region that belongs to neither A nor B is the complement of their union, written as (A ∪ B)′. Since the universal set U contains 45 elements and the union contains 29 elements, the elements outside both sets are n((A ∪ B)′) = n(U) − n(A ∪ B) = 45 − 29 = 16. 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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