Prove that if $G$ is a graph with $n$ vertices and fewer than $n$-1 edges, then $G$ is disconnected.
The book I am working through uses a similar definition of "$n$ vertices and at least $n$-1 edges, then $G$ is connected". They do not provide a proof for that, and now it is asking for the proof of 'fewer than $n$-1 edges, then $G$ is disconnected. I'm not sure how to go about this proof. Any help would be great!