If n(U)=140, n(A′)=58, n(B′)=71, and n(A∩B)=34, what is n(A∪B)?
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Answer and explanation
Correct answer: 117
Use the complement relation n(A)=n(U)−n(A′) and n(B)=n(U)−n(B′). Thus n(A)=140−58=82 and n(B)=140−71=69. Now apply the two-set union formula: n(A∪B)=n(A)+n(B)−n(A∩B)=82+69−34=117. The common elements are subtracted once to avoid double counting, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
117
Why is this the correct answer?
Use the complement relation n(A)=n(U)−n(A′) and n(B)=n(U)−n(B′). Thus n(A)=140−58=82 and n(B)=140−71=69. Now apply the two-set union formula: n(A∪B)=n(A)+n(B)−n(A∩B)=82+69−34=117. The common elements are subtracted once to avoid double counting, so option A 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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