suppose A1, A2,....,A30 are 30 sets each with 5 elements and B1, B2,...., Bn are n sets each with 3 elements. let union ofA1, A2,....,A30 = union ofB1, B2,...., Bn =S. Each element of S belongs to 10 of A's and 9 of B's. find n.

WHAT DOES IT MEAN????????????

Since each Ai has 5 elements and each element of S belong to exactly ten of Ai 'sHence S = 30i = 1 Ai n(S) =110i=130n(Ai) =110×5×30 =15And each of Bj has three element and  each of S belongs to exactly 9  of Bj'sHence S= nj= 1  Bj  n(S) =19j=1nn(Bj) =193n =n3And both n(S) are equal So n3 =15 Or n = 45

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