If n(A∩B′)=29, n(A′∩B)=33, n(A∩B)=17, and n((A∪B)′)=21, what is n(U)?
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Answer and explanation
Correct answer: 100
The universal set is partitioned into four mutually disjoint regions: A∩B′, A′∩B, A∩B, and the outside region (A∪B)′. Every element of U belongs to exactly one of these regions. Therefore, n(U)=29+33+17+21=100. This is a partition count, so no inclusion–exclusion subtraction is needed.
Frequently asked questions
What is the correct answer to this question?
100
Why is this the correct answer?
The universal set is partitioned into four mutually disjoint regions: A∩B′, A′∩B, A∩B, and the outside region (A∪B)′. Every element of U belongs to exactly one of these regions. Therefore, n(U)=29+33+17+21=100. This is a partition count, so no inclusion–exclusion subtraction is needed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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