Hw8 Problem 3

Find all of the left cosets of the subgroup $\langle 3 \rangle$ of $\mathbb{Z_{12}}$.
$0 + \langle 3 \rangle = \{0, 3, 6, 9\}$
$1 + \langle 3 \rangle = \{1, 4, 7, 10\}$
$2 + \langle 3 \rangle = \{2, 5, 8, 11\}$