For each of the following two statements, decide whether it is true or false. If it is true, give a short explanation. If it is false, give a counterexample. (a) Suppose we are given an instance of the Minimum Spanning Tree Problem on a graph G, with edge costs that are all positive and distinct. Let T be a minimum spanning tree for this instance. Now suppose we replace each edge cost ce by its square, c2, thereby creating a new instance of the problem with the same graph but different costs. True or false? T must still be a minimum spanning tree for this new instance. (b) Suppose we are given an instance of the Shortest s-t Path Problem on a directed graph G. We assume that all edge costs are positive and distinct. Let P be a minimum-cost s-t path for this instance. Now suppose we replace each edge cost ce by its square, c2, thereby creating a new instance of the problem with the same graph but different costs. True or false? P must still be a minimum-cost s-t path for this new instance