4. Are the following propositions about digraphs true or false? Justify your answer by giving a proof or a relevant example. (a) The sum of in-degrees of a digraph equals the sum of out-degrees. The in-degree and out-degree of a vertex is its number of incoming and outgoing edges, respectively vertex v the in-degree of v equals the out-degree of v vertex v is n - v and its out-degree is v - (b) There exists a balanced DAG with at least one edge. A digraph is balanced if for every (c) For every n 2 1, there is a digraph with vertices 1,...,n such that the in-degree of