In a DAG, does there exist a sink for all vertices in the DAG?
A sink is a vertex with an out degree of zero. The leaf nodes of a binary search tree are the sinks. This is the trivial case of the statement as a path always exists from a node to itself, this path contains no edges, however the statement never said for vertex $v$, the sink $s$ could not be itself. Without this not only is the statment not true, but for every graph it is untrue since all DAGS have at least one sink and that sink could not be paired with another sink since that defeats the nature of a sinc.