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 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 such that deg (u)-o . 3.B: TRUE/FALSE: "If a graph has at least one vertex u such that deg (u)-o, then the graph must be a DAG 3.C: TRUE/FALSE: "If all vertices u in a given graph have deg (u)>O, then the graph is not acyclic