7 3 Problem 1. (15 points) Perform A* search on the following graph. At each step show (1) the fringe with the corresponding f- values and (2) the explored set. The initial state is vertex "5" and the goal is vertex 4. 9 Heuristics: 2 5 Node 1 = 6 2 Node 2 = 4 1 3 Node 3 = 1 2 1 Node 4 = 0 Node 5 = 14 8 Node 6 = 10 6 5 Node 7 = 15 Node 8 = 15 Node 9 = 10 7 4 Problem 2. (20 points) (1) Is the heuristic in problem 1 admissible? Is it consistent? (2) Suppose you had two heuristics. The first heuristic, h, is admissible and consistent. The second, h2, is admissible but not consistent. Prove or disprove whether a new heuristic defined as: h3 = min(h1, h2), is admissible and/or consistent