You are given the following heuristic function for the Traveling SalesPerson Problem (TSP): h(n) = distance to the closest unvisited city. Answer the following questions:

1. Is this heuristic admissible? Explain your reasoning.

2. Show an example of a TSP where the Greedy-Best-First algorithm with this heuristic finds an optimal solution.

3. Show an example of a TSP where the Greedy-Best-First algorithm with this heuristic does NOT find an optimal solution.

4. Is Greedy-Best-First search with an admissible heuristic guaranteed to find an optimal solution?

5. Propose an admissible heuristics for the TSP, different from the heuristics given above.