Element of Group is in its own Coset

Theorem

Let $G$ be a group.

Let $H$ be a subgroup of $G$.

Let $x \in G$.

Left Coset

Let:

$x H$ be the left coset of $x$ modulo $H$.

Then:

$x \in x H$

Right Coset

Let:

$H x$ be the right coset of $x$ modulo $H$.

Then:

$x \in H x$