Question

If a tree has n nodes how many edges will it have

Answer 1

A tree of n nodes will have n edges.
Suppose the tree with n nodes has n - 1 edges
Let T be the tree with n + 1 nodes
T must have a leaf i.e. a node v such that degv = 1.
Remove v and the 1 edge incident at v
The remainder is a tree which has n vertices
So it has n - 1 edges
Therefore, T must have had (n - 1) + 1 = n edge.