If n(A ∩ B') = 36, n(A' ∩ B) = 44, n(A ∩ B) = 25 and n((A ∪ B)') = 18, then what is n(U)?
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Answer and explanation
Correct answer: 123
The universal set is divided into four mutually exclusive Venn-diagram regions: A only, B only, A ∩ B, and outside A ∪ B. Their given cardinalities are 36, 44, 25, and 18 respectively. Therefore, n(U) = 36 + 44 + 25 + 18 = 123. Each element of U belongs to exactly one of these four regions, so no region is counted twice.
Frequently asked questions
What is the correct answer to this question?
123
Why is this the correct answer?
The universal set is divided into four mutually exclusive Venn-diagram regions: A only, B only, A ∩ B, and outside A ∪ B. Their given cardinalities are 36, 44, 25, and 18 respectively. Therefore, n(U) = 36 + 44 + 25 + 18 = 123. Each element of U belongs to exactly one of these four regions, so no region is counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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