Cosets Partition a Group

Cosets Partition a Group: Let $G$ be a group and let $H\le G$ be a subgroup . Then the set of left cosets $\{gH : g\in G\}$ forms a partition of $G$ (and similarly for right cosets $\{Hg:g\in G\}$).

More precisely: every $g\in G$ lies in the left coset $gH$, and any two left cosets are either equal or disjoint.