Prove A* is admissible. The proof should show that: a. A* search will terminate. b. During its

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Prove A* is admissible.  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.

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