1. True or False? [7 points] Decide whether the following statement is true or false. If it is true, give a short justification. If it is false, give a counterexample. Let G = (V,E) be an arbitrary connected weighted undirected graph with no self-loops (that is, no edges from a vertex to itself), so that the weight of an edge e E E is w(e), and all the weights are distinct. Let e E E be the cheapest edge: that is the edge so that w(e) min w(e). Then there is a minimum spanning tree T of G that contains e * . e EEPlease give long/precise explanation to why it is true or false, thanks

1. True or False? [7 points] Decide whether the following statement is true or false. If it is true, give a short justification. If it is false, give a counterexample. Let G = (V,E) be an arbitrary connected weighted undirected graph with no self-loops (that is, no edges from a vertex to itself), so that the weight of an edge e E E is w(e), and all the weights are distinct. Let e’ E E be the cheapest edge: that is the edge so that w(e) min w(e). Then there is a minimum spanning tree T of G that contains e * . e EE



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