Each set X_r contains 5 elements and each set | vedclass

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(A) The total number of elements (counting repetitions) in $\bigcup_{r=1}^{24} X_r$ is $5 	imes 24 = 120$. Since each element of $S$ belongs to exact

Vedclass · Accepted Answer

$18$

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(A) The total number of elements (counting repetitions) in $\bigcup_{r=1}^{24} X_r$ is $5 	imes 24 = 120$. Since each element of $S$ belongs to exactly $10$ of the $X_r$'s,the number of distinct elements in $S$ is $\frac{120}{10} = 12$. Similarly,for the union $\bigcup_{r=1}^{n} Y_r$,the total number of elements (counting repetitions) is $4n$. Since each element of $S$ belongs to exactly $6$ of the $Y_r$'s,the number of distinct elements in $S$ is $\frac{4n}{6}$. Equating the two expressions for the number of distinct elements in $S$: $12 = \frac{4n}{6}$ $72 = 4n$ $n = 18$.

Each set $X_r$ contains $5$ elements and each set $Y_r$ contains $4$ elements. If $\bigcup_{r=1}^{24} X_r = S = \bigcup_{r=1}^{n} Y_r$,and each element of set $S$ belongs to exactly $10$ of the $X_r$'s and to exactly $6$ of the $Y_r$'s,then find the value of $n$.

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