5. Back to your roots. Let = (y E) be a directed graph. A root of G is a vertex from which every other vertex is reachable (i.e, for every vE V there is a path from r to V). Now suppose G is acyclic. Give an argument for each of the following: (i) if r is a root, then it must have in-degree 0 (i.e., if r has in-degree > 0, then it cannot be a root); (ii) if there is more than one node of in-degree 0, then there is no root; (iii) if there is exactly one node r of in-degree zero, then r is a root Note: this says that in a DAG, there can be at most one root, and that the graph has a root if and only if there is a unique vertex of in-degree zero (in which case, that vertex is the root)