Minimum Spanning Trees (MSTs). (a) Apply Prim's algorithm to find the MST of the graph in Figure 2a starting from vertex a, considering vertices in alphabetical order when there is a choice. Show your work by tracing the algorithm! (Show pi and key array values.) (b) How can we use Prim's algorithm to find a spanning tree of a connected graph with no weights on its edges? Is it a good algorithm for this problem? (c) Now, apply Kruskal's algorithm to find the MST of the graph in Figure 2a. Show your work! (d) Indicate whether the following statements are true or false. Briefly justify your answer: i. If e is a minimum-weight edge in a connected weighted graph, it must be among edges of at least one minimum spanning tree of the graph. ii. If e is a minimum-weight edge in a connected weighted graph, it must be among edges of each minimum spanning tree of the graph. iii. If edge weights of a connected weighted graph are all distinct, the graph must have exactly one minimum spanning tree. iv. If edge weights of a connected weighted graph are not all distinct, the graph must have more than one minimum spanning tree. (a) For Question 4