In a Venn diagram, n(A ∪ B ∪ C) = 215 and n((A ∪ B ∪ C)′) = 35. Exactly two sets have 62 elements. If n(U) is asked, what is the answer?
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Answer and explanation
Correct answer: 250
The universal set U is divided into two disjoint regions: the union A ∪ B ∪ C and its complement (A ∪ B ∪ C)′. Hence n(U) = n(A ∪ B ∪ C) + n((A ∪ B ∪ C)′) = 215 + 35 = 250. The information that exactly two sets have 62 elements is irrelevant to this particular question because the union size is already given.
Frequently asked questions
What is the correct answer to this question?
250
Why is this the correct answer?
The universal set U is divided into two disjoint regions: the union A ∪ B ∪ C and its complement (A ∪ B ∪ C)′. Hence n(U) = n(A ∪ B ∪ C) + n((A ∪ B ∪ C)′) = 215 + 35 = 250. The information that exactly two sets have 62 elements is irrelevant to this particular question because the union size is already given.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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