2. Define a strongly connected component of a graph to be a "sink if there are no edges from it to any other component. (a) (265 students only). Show that the first component found by the strongly connected component algorithm from the lecture is always a sink. (b) (163 students only). Use the answer to part (a) to show that, for every vertex v in every directed graph, v can reach a vertex w that belongs to a sink. (Hint: start the depth-first search at v. You can assume that part (a) is true; you do not have to prove it.) Solution to problem 2 goes here. 2. Define a strongly connected component of a graph to be a "sink if there are no edges from it to any other component. (a) (265 students only). Show that the first component found by the strongly connected component algorithm from the lecture is always a sink. (b) (163 students only). Use the answer to part (a) to show that, for every vertex v in every directed graph, v can reach a vertex w that belongs to a sink. (Hint: start the depth-first search at v. You can assume that part (a) is true; you do not have to prove it.) Solution to problem 2 goes here