For two sets A and B, n(A)=54, n(B)=61, and 73 elements belong to exactly one of the sets. What is n(A∩B)?
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Answer and explanation
Correct answer: 21
The elements belonging to exactly one set are n(A−B)+n(B−A). In terms of the given totals, this is n(A)+n(B)−2n(A∩B), because the common elements are counted in both n(A) and n(B). Thus 73=54+61−2n(A∩B)=115−2n(A∩B). Therefore 2n(A∩B)=42 and n(A∩B)=21.
Frequently asked questions
What is the correct answer to this question?
21
Why is this the correct answer?
The elements belonging to exactly one set are n(A−B)+n(B−A). In terms of the given totals, this is n(A)+n(B)−2n(A∩B), because the common elements are counted in both n(A) and n(B). Thus 73=54+61−2n(A∩B)=115−2n(A∩B). Therefore 2n(A∩B)=42 and n(A∩B)=21.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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