Coset of Trivial Subgroup is Singleton

Theorem
Let $\struct {G, \circ}$ be a group whose identity is $e$.

Let $E := \struct {\set e, \circ}$ denote the trivial subgroup of $\struct {G, \circ}$.

Let $g \in G$.

Then the left coset and right coset of $E$ by $g$ is $\set g$.

Proof
Similarly: