You run DFS on a directed graph G$=($V$,$E$)$ and have access to the pre and post label of each vertex. Check ALL statements that are always true

$1)($u$->$v$)$ is a tree edge if and only if pre$($u$)+1=$pre$($v$).$

$2)($u$->$ u$)$ is a back edge if and only if post$($u$)>$post$($v$).$

$3)$ Your are further given that G is strongly connected. Then there is a

vertex u such that pre$($u$)=1$ and post$($u$)=2$n$.$

$4)$ One can classify the edge $($u$->$v$)$ as tree edge, forward edge, back edge, or cross edge once we know the numbers pre$($u$),$ post$($u$),$ pre$($v$),$ post$($v$).$