Let $G$ be any undirected graph with positive edge weights, and $T$ be a minimum spanning tree of $G$. For any two vertices, $u$ and $v$, let $d_1(u, v)$ and $d_2(u, v)$ be the shortest distances between $u$ and $v$ in $G$ and $T$, respectively. Which ONE of the options is CORRECT for all possible $G$, $T$, $u$ and $v$?

Since $T$ is a spanning tree of $G$, the edge set of $T$ is a subset of the edge set of $G$, i.e., $E(T) \subseteq E(G)$.

• The path between any two vertices $u$ and $v$ in $T$ is also a valid path between $u$ and $v$ in $G$.

• The shortest distance $d_1(u, v)$ in $G$ is the minimum weight across all possible paths between $u$ and $v$ in $G$.

• Because all paths in $T$ are contained in $G$, the minimum path length in $G$ can never exceed the path length in $T$.

Therefore, for all possible graphs $G$, spanning trees $T$, and pairs of vertices $u, v$, we always have:

Hence, (B) is the correct option.