(a) (10 points) In the depth first algorithm, let T be a tree after stopping the algorithm. Show that for every arc which is not included in T like (m,n), either node m is an ancestor of node n in T or node n is an ancestor of m in T. By a counter-example, show that a breadth first tree doesn't have this property. (b) (10 points) Show that a path from the source node to any other node ; is the shortest path in a breadth-first search tree