can you answer these questions

Consider an undirected connected graph G : (V, E) with edge costs (36 > 0 for e E E which are all distinct. (a) Let E' C; E be dened as the following set of edges: for each node v, E ' contains the cheapest of all edges incident on v, i.e., the cheapest edge that has '0 as one of its endpoints. Is the graph (V, E ' ) connected? Is it acyclic? For both questions, provide a proof or a counter-example with explanations. (b) Consider the following outline for an algorithm, which starts with an empty set T of edges: Let E' contain the cheapest edge out of each connected component of (V, T). Add E' to T, and repeat until (V, T) is connected. Show that this algorithm outputs a minimum spanning tree of G, and can be implemented in time 0 (m log 7:) Hints : 0 Each iteration of this algorithm can be Viewed as applying the operation from part (a) on a \"contracted graph\