Let $F$ be a minimal edge-cut of a connected multigraph $G=(V,E)$. Prove that there exists a subset $U$ of $V$ such that $F$ is precisely the set of edges that join a vertex in $U$ to a vertex in the complement $\overline U$ of $U$.
An edge-cut of $G$ is a set $F$ of edges whose removal disconnects $G$.
An edge-cut $F$ is minimal provided that no subset of $F$ other than $F$ itself is an edge-cut.
My Attempt: I am frankly not sure how to approach this problem. It requires an existence proof so do I need to construct a set $U$ or do I need to indirectly show that such a set exists? Any hints will be much appreciated.