GATE | GATE CS Mock 2018 | Question 37

Let G = (V, E) be any connected undirected edge-weighted graph. The weights of the edges in E are positive. Consider the following statements:

1. The path between a pair of vertices in a minimum spanning tree of an undirected graph is necessarily the shortest (minimum weight) path.
2. Minimum Spanning Tree of G is always unique and shortest path between a pair of vertices may not be unique.

Which of the above statements is/are necessarily true?