# Each set Xr contains 5 elements and each set Yr contains 2 elements and ⋃r=120Xr=S=⋃r=1nYr If each element of S belong to exactly 10 of the Xr’s and to exactly 4 of the Yr’s, then n is ______. - Mathematics

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Each set Xr contains 5 elements and each set Yr contains 2 elements and $\bigcup\limits_{r=1}^{20} X_{r} = S = \bigcup\limits_{r=1}^{n} Y_{r}$ If each element of S belong to exactly 10 of the Xr’s and to exactly 4 of the Yr’s, then n is ______.

• 10

• 20

• 100

• 50

#### Solution

Each set Xr contains 5 elements and each set Yr contains 2 elements and $\bigcup\limits_{r=1}^{20} X_{r} = S = \bigcup\limits_{r=1}^{n} Y_{r}$ If each element of S belong to exactly 10 of the Xr’s and to exactly 4 of the Yr’s, then n is 20.

Explanation:

Since, "n"("X"_"r") = 5

$\bigcup\limits_{r=1}^{20} X$ = S

We get n(S) = 100

But each element of S belong to exactly 10 of the "X"_"r"'s

So, 100/10 = 10 are the number of distinct elements in S.

Also each element of S belong to exactly 4 of the Yr’s and each Yr contain 2 elements.

If S has n number of Yr in it.

Then (2"n")/4 = 10

Which gives n = 20

Concept: Operations on Sets - Union Set
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 1 Sets
Solved Examples | Q 14 | Page 11