You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Cardinality of Sets

Suppose A 1, ...

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 having 3 elements. Let each element of S belongs to exactly 10 of $A_{i}^{'}$ s and exactly 9 of $B_{i}^{'}$ s. Then, find the value of n.

Open in App

Solution

If elements are not repeated, then number of elements in $A_{1} \cup A_{2} \cup A_{3} \cup . . . \cup A_{30}$ is $30 \times 5$ but each element is used 10 times.

So, $S = \frac{30 \times 5}{10} = 15 . . . (i)$

Similarly, if elements in $B_{1}, B_{2}, . . ., B_{n}$ are not repeated, then total number of elements in 3n, but each element is repeated 9 times.

So, $S = \frac{3 n}{9}$

$\Rightarrow 15 = \frac{3 n}{9}$ [from Eq. (i)]

$\Rightarrow n = \frac{15 \times 9}{3} = 45$

Suggest Corrections

Similar questions

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 $⋃_{r = 1}^{30}$ = $⋃_{f = 1}^{n} B_{j} = S$ and each of S belongs to exactly 10 of the $A_{i}^{^{'} s}$ and exactly 9 of the $B_{i}^{^{'} s}$ , 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

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

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} . . . . . 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

Join BYJU'S Learning Program

Suppose A1,A2,...,A30 are thirty sets each having 5 elements and B1,B2,...,Bn are n sets each having 3 elements. Let each element of S belongs to exactly 10 of A′i s and exactly 9 of B′i s. Then, find the value of n.

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 having 3 elements. Let each element of S belongs to exactly 10 of $A_{i}^{'}$ s and exactly 9 of $B_{i}^{'}$ s. Then, find the value of n.