1. True or False: (give the reason)
   1. The solution path found by Uniform-Cost search may change if we add the same positive constant, c, to every edge cost.
   2. Graph search with the A* algorithm is optimal when the heuristic function is admissible but not consistent.
   3. If a heuristic is admissible, it is also consistent (aka monotonic).
   4. If h₁ is an admissible heuristic and h₂ is not an admissible heuristic, (h₁ + h₂)/2 must be an admissible heuristic.
   5. Greedy Best-First search with an admissible heuristic is guaranteed to find an optimal solution.