PROBLEM 3 (24 points): A Directed-Acyclic Graph is exactly what the name suggests: a directed graph with no cycles For a directed graph G = (V, E) , let deg (u) represent the out-degree of vertex u E V-ie, the number edges for which u is the source vertex. Below are some TRUE/FALSE questions. When you answer FALSE, give a counter-example; when you answer TRUE, give a proof of the statement's correctness. Your proof can be informal so long as it is correct and convincing. 3.A: TRUE/FALSE: If a graph is a DAG, then there exists at least one vertex u that deg (u)=0 . such 3B: TRUE/FALSE: "If a graph has at least one vertex u such that deg (u) =0, then the graph must be a DAG 3.C: TRUE/FALSE: If all vertices u is not acyclic in a given graph have deg(u)>0, then the graph