Prove the optimality of the reverse-delete minimum spanning tree algorithm using the cut property and the cycle property (in the same manner the optimality of each of the Prims algorithm and the Kruskals algorithm was proven in class.) Specifically, prove each of the following two cases of alternative actions taken by the algorithm: (case 1) do not delete an edge when it would disconnect the graph and (case 2) delete an edge when it would not disconnect the graph. Your proof in each case should clearly state which property justifies the action and why.