Any help with these would be greatly appreciated and detailed explanations would

Question

Any help with these would be greatly appreciated and detailed explanations would be really great! Thank you!

For the following assertions, judge whether it is true or false. Justify your answers with an explanation, examples or counterexamples.

a) The input to an agent program is the same as the input to the agent function.

b) Suppose an agent selects its action uniformly at random from the set of possible actions. There exists a deterministic task environment in which this agent is rational.

c) Breadth-first search is complete in the finite space with repeated state check even if zero stepcosts are allowed.

d) h(n) = 0 is an admissible heuristic for any problem.

e) Uniform cost search is a special case of A* search with h(n) = c for any state n.

f) In a game tree, Minimax algorithm and - pruning algorithm can sometimes return a different results.

g) Depth first search always expands at least as many nodes as A* search with an admissible heuristic.

h) Missionaries and cannibals problem is a constraint satisfaction problem so that we can solve it by a local search algorithm such as hill-climbing algorithm

Explanation / Answer

a) The input to an agent program is the same as the input to the agent function.
       False. The input to a agent function is the percept history. The input to a agent
program is only the current percept; it is up to the agent program to record any
relevant history needed to make actions.

b) Suppose an agent selects its action uniformly at random from the set of possible actions. There exists a deterministic task environment in which this agent is rational.
   True. Again consider the ”all actions always give equal reward” case

c) Breadth-first search is complete in the finite space with repeated state check even if zero stepcosts are allowed.
   TRUE, because if there exists a goal it occurs at finite depth d and will be found in O(bd) steps. “Complete” means “will find a goal when one exists” --- and does NOT imply “optimal,” which
means “will find a lowest-cost goal when one exists.” Thus, the step costs are irrelevant to “complete.”

d) h(n) = 0 is an admissible heuristic for any problem.
   TRUE. h(n)=0 NEVER over-estimates the remaining optimal distance to a goal node.
  
e) Uniform cost search is a special case of A* search with h(n) = c for any state n.
   False. Uniform-cost search can be a special case of A* search if you have h(n) = 0.
  
f) In a game tree, Minimax algorithm and pruning algorithm can sometimes return a different results.
   False. Pruning is a sound optimization in that it does not change the score of the result of the algorithm it optimizes.
So, the value does not change. But the concrete realization of it can be different.
  
g) Depth first search always expands at least as many nodes as A* search with an admissible heuristic.
   FALSE. Depth-first search may possibly, sometimes, BY GOOD LUCK, expand fewer nodes
than A* search with an admissible heuristic. E.g., it is logically possible that sometimes, by good
luck, depth-first search may march directly to the goal with no back-tracking.
  
h) Missionaries and cannibals problem is a constraint satisfaction problem so that we can solve it by a local search algorithm such as hill-climbing algorithm
   False. Missionaries and cannibals come under uniformed search where no problem specific information will be provided. On the other hand, hill-climbing is informed search wherein proble specific info will be given

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