If only A has 38 elements, only B has 35 elements, only C has 29 elements, exactly two sets together have 47 elements, and all three sets have 14 elements, what is n(A∪B∪C)?
Answer and explanation
Correct answer: 163
The union is obtained by adding all mutually exclusive regions of the three-set Venn diagram. These regions are: only A with 38 elements, only B with 35, only C with 29, exactly two sets with 47, and all three sets with 14. Hence n(A∪B∪C) = 38 + 35 + 29 + 47 + 14 = 163. No region is counted twice.
Frequently asked questions
What is the correct answer to this question?
163
Why is this the correct answer?
The union is obtained by adding all mutually exclusive regions of the three-set Venn diagram. These regions are: only A with 38 elements, only B with 35, only C with 29, exactly two sets with 47, and all three sets with 14. Hence n(A∪B∪C) = 38 + 35 + 29 + 47 + 14 = 163. No region is counted twice.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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