Suppose A1- A2-A30 are thirty sets each having 5 elements and B1- B2-Bn are n sets each with 3 elements- let -i-130Ai-j-1nBj - S and each element of S belongs to exactly 10 of Ai-S and exactly 9 of the Bj-S- Then n is equal to

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Standard IX

Mathematics

Union

Suppose A1, A...

Question

Suppose $A_{1}, A_{2}, . . . . . . . . . . . . . . . . . . . . . A_{3} 0$ are thirty sets each having 5 elements and $B_{1}, B_{2}, . . . . . . . . . . . . . . . . B_{n}$ are n sets each with 3 elements, let $30 ⋃ i = 1$ $A_{i}$ = $n ⋃ j = 1$ $B_{j} = S$ and each element of S belongs to exactly 10 of $A_{i}$ 'S and exactly 9 of the $B_{j}$ 'S. Then $n$ is equal to

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Solution

The correct option is C
45

Since S = $30 ⋃ i = 1$ $A_{i}$

Now, element in the union S belongs to exactly 10 of the $A_{i}$ 'S. So n(S) = $\frac{1}{10} (5 \times 30)$ =15 Again, S = $n ⋃ j = 1$ $B_{j}$

So, n(S) = $\frac{1}{9} (3 \times n)$ = $\frac{n}{3}$ Thus, $\frac{n}{3}$ = 15 $∴$ n = 45

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Similar questions

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

Q. Suppose

A_{1}, A_{2}, \dots, A_{30}

are thirty sets each having

5

elements and

B_{1}, B_{2}, \dots, B_{n}

are

n

sets each with

3

elements, let

30 ⋃ i = 1 A_{i} = n ⋃ 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

Q. Suppose

A_{1}, A_{2} . . . . . A_{30}

are thirty sets having 5 elements and

B_{1}, B_{2} . . . . B_{n}

are n sets each with 3 elements. Let

30 ⋃ i = 1 A i = n ⋃ i = 1 B j = S

and each elements of S belongs to exactly 10 of the Ai's and exactly 9 of the Bj's. Then n is equal to

Suppose A1,A2,.....................A30 are thirty sets each having 5 elements and B1,B2,................Bn are n sets each with 3 elements, let $30 ⋃ i = 1$ $A_{i}$ = $n ⋃ j = 1$ $B_{j}$ = S and each element of S belongs to exactly 10 of $A_{i}$ 'S and exactly 9 of the $B_{j}$ 'S. Then n is equal to

Q. 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

\cup_{i = 1}^{30} A_{i} = \cup_{j = 1}^{n} B_{j} = S

and each element of S belong to exactly 10 of the

A_{i}' s

and exactly 9 of the

B_{j}' s

, then n is equal to

(a) 15 (b) 3 (c) 45 (d) 35

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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 Ai'S and exactly 9 of the Bj'S. Then n is equal to

The correct option is C 45 Since S =30⋃i=1Ai Now, element in the union S belongs to exactly 10 of the Ai'S. So n(S) = 110(5×30)=15 Again, S =n⋃j=1Bj So, n(S) = 19(3×n) = n3 Thus,n3 = 15 ∴ n = 45

The correct option is C
45

Since S = $30 ⋃ i = 1$ $A_{i}$

Now, element in the union S belongs to exactly 10 of the $A_{i}$ 'S. So n(S) = $\frac{1}{10} (5 \times 30)$ =15 Again, S = $n ⋃ j = 1$ $B_{j}$

So, n(S) = $\frac{1}{9} (3 \times n)$ = $\frac{n}{3}$ Thus, $\frac{n}{3}$ = 15 $∴$ n = 45