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in Sets, Relations and Functions by (30.2k points)
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Suppose A1, A2,...,A30 are thirty sets each having 5 elements and B1, B2,...,Bn are n sets each with 3 elements, let \(U_{i=1}^{30}\) = \(U_{j=1}^{n}\) Bj = s and each element of S belongs to exactly 10 of the Ai.s and exactly 9 of the Bj.s , then n is equal to 

A. 15 

B. 3 

C. 45 

D. 35

1 Answer

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Best answer

If elements are not repeated then number of elements inA1⋃A2⋃A3⋃….⋃A30 = 30*5=150 

But, each element of S is in 10 of Ai

∴ s = \(\frac{150}{10}\) = 15.

If elements are not repeated then number of elements in B1⋃B2⋃B3⋃….⋃Bn=3*n 

But, each element of S is in 9 of B1

∴ s = \(\frac{3\times{n}}{9}\)

 ∴ s = \(\frac{3\times{n}}{9}\) = 15

∴ 3 × n =15 × 9 

∴ n = 45

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