For each group $G$ and subgroup $H$ determine if elements $\#1$ and $\#2$ represent the same left $H$-coset in $G$.

($U(n)$ is the multiplicative group of units in $\mathbb{Z}_n$ and $Q_8$ is the quaternion group.)

$G$	$H$	Element $\#1$	Element $\#2$	Answer (Y/N)
$\mathbb{Z}_{22}$	$\langle 15 \pmod{22} \rangle$	$5$	$19$
$U(22)$	$\langle 15 \pmod{22} \rangle$	$5$	$19$
$Q_8$	$\langle k \rangle$	$j$	$i$
$Q_8$	$\langle -1 \rangle$	$j$	$-k$