Prove A* is admissible. Hint: the proof should show that: a. A* search will terminate. b. During its execution there is always a node on open that lies on an optimal path to the goal. c. If there is a...

Prove A* is admissible. Hint: the proof should show that:

a. A* search will terminate.

b. During its execution there is always a node on open that lies on an optimal path to the goal.

c. If there is a path to a goal, A* will terminate by finding the optimal path.