For each of the following assertions, say whether it is true or false and support your answer with examples or counterexamples where appropriate.

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

b$.$ There exist task environments in which no pure reflex agent can behave rationally.

c$.$ There exists a task environment in which every agent is rational.

e$.$ Every agent function is implementable by some program$/$machine combination.

f$.$ 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.

g$.$ It is possible for a given agent to be perfectly rational in two distinct task environments.

i$.$ A perfectly rational poker$-$playing agent never loses.

j$.$ For a simple reflex agent in a partially observable environment, a randomized policy can outperform any deterministic policy.

k$.$ There is a model$-$based reflex agent that can remember all of its percepts.

I. Suppose agent $A1$ is rational and agent $A2$ is irrational. There exists a task environment where $A2\text{'}$s actual score will be greater than A$1\text{'}$s actual score.

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