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 sense only partial information about the state can not be perfectly rational

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

c$.$ There exits a task enviorment in which every agent is rational.

d$.$ The input to an agent program is the same as the input to the agent function.

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

f$.$ Suppose an agent selcts its action uniformaly at random from the set of possible actions. There exists a deterministic task enviorment in which this agent is rational.

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

h$.$ Every agent is rational in an unobservable enviorment.

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