Answer all of the following:
(a) Give an example of a weighted connected graph G = (V,E) and a vertex v, such that the minimum spanning tree of G is the same as the shortest-path spanning tree rooted at v.
(b) Give an example of a weighted connected directed graph G = (V,E) and a vertex v, such that the minimum-cost spanning tree of G is very different from the shortest-path spanning tree rooted at v.
(c) Can the two trees be completely disjointed?