In a two-set Venn diagram, n(A−B)=18, n(A∩B)=14, n(B−A)=21, and 7 elements are outside both sets. What is n(U)?
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Answer and explanation
Correct answer: 60
A two-set Venn diagram is divided into four mutually exclusive regions: A−B, A∩B, B−A, and the region outside A∪B. The universal set contains every one of these regions. Therefore, n(U)=18+14+21+7=60. Since no region overlaps another in this partition, each value is added exactly once. Thus, option C is correct.
Frequently asked questions
What is the correct answer to this question?
60
Why is this the correct answer?
A two-set Venn diagram is divided into four mutually exclusive regions: A−B, A∩B, B−A, and the region outside A∪B. The universal set contains every one of these regions. Therefore, n(U)=18+14+21+7=60. Since no region overlaps another in this partition, each value is added exactly once. Thus, option C 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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