If n(A)=52, n(B)=47, and n(A∪B)=79, what is n(A∩B)?
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Answer and explanation
Correct answer: 20
Use the two-set inclusion–exclusion identity n(A∪B)=n(A)+n(B)−n(A∩B). Rearranging gives n(A∩B)=n(A)+n(B)−n(A∪B). Substitution yields 52+47−79=99−79=20. The common elements must be subtracted because adding the two set totals counts them twice. Therefore, option B is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
Use the two-set inclusion–exclusion identity n(A∪B)=n(A)+n(B)−n(A∩B). Rearranging gives n(A∩B)=n(A)+n(B)−n(A∪B). Substitution yields 52+47−79=99−79=20. The common elements must be subtracted because adding the two set totals counts them twice. Therefore, option B is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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