If spanning tree then connected?

Question

If $T$ is a spanning tree of $G$ does that mean $G$ is connected?

In generally does this have to be true? I am inclined to believe no because we can skip some edge?

Answer 1

If you can find a spanning tree over $G$ then you are able to connect all the vertices of $G$ so $G$ is connected. A graph that is not connected will not contain a spanning tree.