Graph and MST, Some Facts and Validity

问题

My notes tell me that the first and last is false. I need some idea of how to understand the validity of these sentences in a more simple and concise manner.

Suppose M is an MST (minimum spanning tree) of the Weighted Graph - GR.

1. Let A be a vertex of GR then M-{A} is also MST of GR-{A}.

2. Let A be a leaf of M then M-{A} is also MST of GR-{A}.

3. If e is a edge of M then (M-{e}) is a forest of M1 and M2 trees such that for M_i, i=1,2 is a MST of Induced Graph GR on vertexes T_i.

来源：https://stackoverflow.com/questions/65102458/graph-and-mst-some-facts-and-validity