Suppose A1 - A2- A30 are thirty sets each having 5 elements and B1- B2- Bn are n sets each with 3 elements - let i - 130- Ai - j - 1n- 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

The correct option is A 45If elements are not repeated then the number of elements in A_1∪ A_2∪ A_3∪ A_30 is 30× 5 But each elements is used 10 time ...

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Standard XII

Mathematics

Definition of Sets

Suppose A1 ...

Question

Suppose $A_{1}, A_{2}, . . . A_{30}$ are thirty sets each having 5 elements and $B_{1}, B_{2}, . . ., B_{n}$ are n sets each with 3 elements , let $30 \cup i = 1 A_{i} = n \cup j = 1 B_{j} = S$ and each element of S belongs to exactly 10 of the $A_{i}^{'} s$ and exactly 9 of the $B_{j}^{'} S$ . then n is equal to

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Solution

The correct option is A 45
If elements are not repeated then the number of elements in $A_{1} \cup A_{2} \cup A_{3} \cup A_{30}$ is $30 \times 5$
But each elements is used 10 times
so, $S = \frac{30 \times 5}{10} = 15$
If the elements in $B_{1}, B_{2}, . . . . ., B_{n}$ are not repeated.
then total number of element in
$B_{1} \cup B_{2} \cup B_{3} . . . . . \cup B_{n}$ is 3n
but each elements is repeated 9 times
so,
$S = \frac{3 n}{9} = 15 = \frac{3 n}{9}$
$n = 45$

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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 30∪i=1Ai=n∪j=1Bj=S and each element of S belongs to exactly 10 of the A′is and exactly 9 of the B′jS. then n is equal to