In a Venn diagram, n(U)=90, n(A)=46, n(B)=38, and n(A∩B)=16. What is n(A∪B)?
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Answer and explanation
Correct answer: 68
For two finite sets, the union formula is n(A∪B)=n(A)+n(B)−n(A∩B). The intersection is subtracted because elements common to A and B are counted once in n(A) and once again in n(B). Therefore, n(A∪B)=46+38−16=68. The universal-set size is not needed for this calculation. Thus, option B is correct.
Frequently asked questions
What is the correct answer to this question?
68
Why is this the correct answer?
For two finite sets, the union formula is n(A∪B)=n(A)+n(B)−n(A∩B). The intersection is subtracted because elements common to A and B are counted once in n(A) and once again in n(B). Therefore, n(A∪B)=46+38−16=68. The universal-set size is not needed for this calculation. Thus, option B 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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