Let $G= U_{32}$ and $ K = \langle9 \rangle$. Determine whether the following cosets are identical or disjoint:
(a) $K17$ and $K19$
(b) $K9$ and $K25$
For part (a), So far I know $G$ is the set of units in $\mathbb Z/32\mathbb Z$ which is $\{1,3,5,7,\dots,31\}$ and I have K is the set $\{9,17,25,1\}$ A little lost on what I am looking for next
Is it enough to say that since $K17$ and $K19$ are both not in the set $K$, that they are disjoint? And in part (b), since $K9$ and $K25$ are both in $K$, they are identical?
Since $17\in K$, $K17=K$. And, since $19\notin K$, $K19\neq K$. And since $K17\neq K19$, they are disjoint (two cosets are either identical or disjoint).
On the other hand, $K9=K25=K$.