Proving Lagrange's Theorem

Show that if $G$ is any group (not necessarily finite) and $H$ is a subgroup, then $G$ is a disjoint union of left cosets of $H$ .
State and prove Lagrange's Theorem for finite groups.

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\begin{enumerate}[label=(\alph*)]
	\item Show that if $G$ is any group (not necessarily finite) and $H$ is a subgroup, then $G$ is a disjoint union of left cosets of $H$.
	\item State and prove Lagrange's Theorem for finite groups.
\end{enumerate}