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Part I: True or False Problem $(3$ points each, $18$ points in total$)$

$(1)$ An agent that senses only partial information about the state cannot be perfectly rational.

$(2)$ There exists a task environment in which every agent is rational.

$(3)$ Suppose agent A$1$ is rational and agent A$2$ is irrational. There exists a task environment where A$2$s actual score will be greater than A$1$s actual score.

$(4)$ h$($n$)=0$ is an admissible heuristic for the $8-$puzzle.

$(5)$ A$*$ is of no use in robotics because percepts, states, and actions are continuous.

$(6)$ Breadth$-$first search is complete even if zero step costs are allowed.

Part II: Short answer problems $(4$ points each, $12$ points in total$)$

For each of the following activities, give a description of the task environment. For example, playing soccer: partially observable, stochastic, sequential, dynamic, continuous, multi$-$agent.

$(1)$ Playing a tennis match

$(2)$ Practicing tennis against a wall

$(3)$ Performing a high jump