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## Homework Statement

Show that the subgroup of ##D_{2n}## generated by the set ##\{s, rs \}## is ##D_{2n}## itself. (i.e. show that ##\{s, rs\}## is another set of generators different than ##\{r,s\}##).

## Homework Equations

## The Attempt at a Solution

It's not clear to me what exactly I need to do. Just as some background, I have it defined that if ##G## is a group and ##X \subseteq G## then ##\langle X \rangle = \{x^{j_1}_1x^{j_2}_2 \dots x^{j_m}_m ~|~ m, j_1, \dots, j_m \in \mathbb{Z}, x_1 \dots, x_m \in X\}##. Will this definition be useful to me? Using the definition do I need to show that ##\langle s, rs \rangle = \langle r, s \rangle##?

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