In three sets, n(A∩B)=31, n(B∩C)=29, n(C∩A)=25, and n(A∩B∩C)=12. How many elements are in exactly two sets?
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Answer and explanation
Correct answer: 49
Each pairwise intersection includes the elements that lie in all three sets. Therefore, the regions belonging to exactly two sets are A∩B only: 31−12=19, B∩C only: 29−12=17, and C∩A only: 25−12=13. Adding these disjoint regions gives 19+17+13=49. Thus exactly 49 elements belong to two sets and not to the third.
Frequently asked questions
What is the correct answer to this question?
49
Why is this the correct answer?
Each pairwise intersection includes the elements that lie in all three sets. Therefore, the regions belonging to exactly two sets are A∩B only: 31−12=19, B∩C only: 29−12=17, and C∩A only: 25−12=13. Adding these disjoint regions gives 19+17+13=49. Thus exactly 49 elements belong to two sets and not to the third.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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