Let $G=(V,E,w)$ be an undirected, weighted, simple, and connected graph. Let $T_1$ and $T_2$ be two minimum spanning trees of $G$. Define the set of edges $F \subseteq E$ as all edges that are in either $T_1$ or $T_2$ but not in both. Suppose that $F \ne \emptyset$. Select all correct statement(s) below.