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 $v$ ?

Let G be a connected undirected weighted graph. Consider the following two statements.

S₁: There exists a minimum weight edge in G which is present in every minimum spanning tree of G.

S₂: If every edge in G has distinct weight, then G has a unique minimum spanning tree. Which one of the following options is correct?

$$P:$$ Minimum spanning tree of $$G$$ does not change
$$Q:$$ Shortest path between any pair of vertices does not change