In a Venn diagram, n(A∪B)=98 and n(A∩B)=42. How many elements belong to exactly one of the two sets?
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Answer and explanation
Correct answer: 56
The union contains elements in A only, B only, and both sets. The elements belonging to exactly one set are obtained by removing the common region from the union: n(exactly one)=n(A∪B)−n(A∩B)=98−42=56. Thus option A is correct. The value 98 includes the intersection, while 42 counts only the common region.
Frequently asked questions
What is the correct answer to this question?
56
Why is this the correct answer?
The union contains elements in A only, B only, and both sets. The elements belonging to exactly one set are obtained by removing the common region from the union: n(exactly one)=n(A∪B)−n(A∩B)=98−42=56. Thus option A is correct. The value 98 includes the intersection, while 42 counts only the common region.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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