Question

asd

Answer 1

e=n-1 is actually one of the definitions of a tree, so we're running in circles!

However, if you want, try the following:
Given
-A connected graph which is a tree
This implies that there are no cycles, and at least two leaves (a leaf is a vertex of degree one, i.e. with exactly one adjacent edge).

Case A:
If the graph has exactly two vertices connected by an edge, then there are 2 vertices and 1 edge, thus e=n-1.
Case B:
If the n>2, then remove any leaf, together with the adjacent edge. So there are n-1 vertices and e-1 edges.
Repeat above until there are only two vertices left, which satisfies e=n-1.
Therefore e=n-1 is satisfied by a tree of any number of vertices n.