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Suppose A1,A2….. A(30) are thirty sets e...

Suppose `A_1,A_2….. A_(30)` are thirty sets each having 5 elements and `B_1B_2…..B_n` are n sets each having 3 elements ,Let `overset(30)underset(i=1)bigcupA_1=overset(n)underset(j=1)bigcupB_j=s`
and each element of S belongs to exactly 10 of the `A_1` and exactly 9 of the value of n.

Text Solution

Verified by Experts

If elements are not repeated , then number of elements in `A_1 cup A_2 cup A_3 ……cup A_30 xx5 =150 .`
but each elements of S is used 10 times in `A_i` s so
`s=(30xx5)/(10)`
If elements in `B_1 cup B_2 cup B_3 ….cup B_n` is 3n But each elements of S is repeated 9 time in `B_j` s so
`S=(3n)/(9) rArr 15 = (3n)/(9)`
`therefore n=45`
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