In each of the following problems you are given a subgroup $H$ of a group $G$, and pairs of elements $x,y \in G$. Determine if $x$ and $y$ belong to the same left $H$-cosets.
Answer Y (for "yes") or N (for "no").

(i) $G = \mathbb{Z}$; $H = 10 \mathbb{Z}$

	$x=6, y=16$	$x=4,y=14$	$x=8,y=13$
$x+H = y+H$ ?

(ii) $G = D_{6}$, dihedral group of order 12 with generators $a$, $b$ where $a^{6} = b^{2} = e$ and $ba = a^{-1}b$;
$H = \langle a^{4} b^{1} \rangle$.

	$x=a, y=b^{1}$	$x=b, y=a^{2} b$	$x=b^{1} a^{4}, y=a^{-2}$
$xH = yH$ ?