prove that a connected graph with $n$ vertices has at least $n-1$ edges Show that every connected graph with $n$ vertices has at least $n − 1$ edges.
How can I prove this?  Conceptually, I understand that the following graph has 3 vertices, and two edges:
a-----b-----c
with $a$, $b$ and $c$ being vertices, and $\{a,b\}$, $\{b,c\}$ being edges.
Is there some way to prove this logically?
--UPDATE--
Does this look correct?  Any advice on how to improve this proof would be appreciated.  Thank you.


Hint: Let $\Gamma$ be a connected graph. If $T \subset \Gamma$ is a maximal subtree, then $|E(\Gamma)| \geq |E(T)|$ and $|V(\Gamma)|=|V(T)|$. (Where $E(\cdot)$ and $V(\cdot)$ is the set of edges and vertices respectively.)
