Mathematical induction proof that each tree has $k = m − 1$ edges

Question

How to prove via Mathematical induction (over the number of edges $l\geq 0$):

$$\text{For each tree } G = (V, E): k = m − 1.$$

$(m = \#V, k = \#E)$.

Answer 1

Basis: A tree with one vertex ($m = 1$) has $0$ edges ($k = m -1$).

Induction step: Every time you add an edge, you increase $k$ by $1$ and $m$ by $1$ (since you attach the new edge to a previous vertex, leaving only one new vertex), so you still have $k = m - 1$.