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U1,U2,...U15 assets each containing two elements and each belongs to three sets V1,V2...V10 are 10 sets all having same cardinal number `n` and each element belongs to four sets

U1,U2,...U15 assets each containing two elements and each belongs to three sets V1,V2...V10 are 10 sets all having same cardinal number `n` and each element belongs to four sets

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Grade:12

1 Answers

Shubham Kumar Gupta Ggps
42 Points
6 years ago
This is a "double-counting" problem.U1,U2,...,U15have a total of 30 elements, if you ignore duplicates. It has a total of x unique elements, such that |U1∪U2∪…U15|=xV1,V2,...,V10 have a total of 10n elements, if you ignore duplicates. It also has a total of x unique elements, such that |V1∪V2∪…V10|=xEach of the x elements belongs to three of Ui and four of Vj. So, 3x=30 and 4x=10n. Then, x=10 and n=4

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