True or false: trees $(15$ points$)$

Check the box next to each statement that is true for all n$-$vertex graphs G$.$

$\backslash$geoquad If G is bipartite, then G has a spanning tree.

$\backslash$geoquad If G has a spanning tree, then G is connected.

$\backslash$geoquad If edge vw is a bridge of G$,$ then G has only one v$$ w path.

$\backslash$geoquad If G is connected and has at most n$1$ edges, then G is a tree.

$\backslash$geoquad If G is acyclic and has at least n$1$ edges, then G is a tree.