Problem 3: In an undirected graph G with vertex set V and edge set E, the degree d(u) of a node u is the number of neighbors that u has (i.e., the number of nodes that u is linked to). In a directed graph, a node u has an indegree, which counts the number of incoming edges, and an outdegree, which counts the number of outgoing edges. 1. Show that in an undirected graph, uevd(u) = 2E1. Here, repre- sents the size of the edge set E: in other words, the number of edges. 2. Show that in an undirected graph, there must be an even number of vertices with odd degree 3. Is it true that in a directed graph, there must be an even number of vertices with odd indegree? If ves, prove your answer. If no, give an example showing where this does not hold