If n(A∩B)=42, n(A∩C)=36, n(B∩C)=34, and n(A∩B∩C)=15, how many elements are in at least two sets?
Answer and explanation
Correct answer: 82
The elements in exactly two sets are found by removing the triple intersection from each pairwise intersection: (42−15)+(36−15)+(34−15)=27+21+19=67. The elements in all three sets, numbering 15, must then be added once. Therefore, the number in at least two sets is 67+15=82. This wording includes both exactly two and all three sets.
Frequently asked questions
What is the correct answer to this question?
82
Why is this the correct answer?
The elements in exactly two sets are found by removing the triple intersection from each pairwise intersection: (42−15)+(36−15)+(34−15)=27+21+19=67. The elements in all three sets, numbering 15, must then be added once. Therefore, the number in at least two sets is 67+15=82. This wording includes both exactly two and all three sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
