The set ${\frac{7}{8}, \frac{8}{9}, \frac{9}{10}, \frac{10}{11}, \frac{11}{12}}$ expressed in set-builder form is ____. (Here, N represents the set of natural numbers.)

${x : x = \frac{n}{n + 1}, n \in N, 7 < n < 11}$

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${x : x = \frac{7 n}{7 n + 1}, n \in N}$

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${x : x = \frac{n}{n + 1}, n \in N}$

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${x : x = \frac{n}{n + 1}, n \in N, 7 \leq n \leq 11}$

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Solution

The correct option is D
${x : x = \frac{n}{n + 1}, n \in N, 7 \leq n \leq 11}$

${\frac{7}{8}, \frac{8}{9}, \frac{9}{10}, \frac{10}{11}, \frac{11}{12}} = {\frac{7}{7 + 1}, \frac{8}{8 + 1}, \frac{9}{9 + 1}, \frac{10}{10 + 1}, \frac{11}{11 + 1}}$

This can be represented in the set-builder form as
${x : x = \frac{n}{n + 1}, n \in N, 7 \leq n \leq 11},$
where N stands for the set of natural numbers.

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