For each of the following statements, indicate if the statement is True or False. If True, provide an example demonstrating that it is True. If False, provide a counterexample.

a). An agent that sense only partial information about the state cannot be perfectly rational.

b) There exist task environments in which no pure reflect agent can behave rationally.

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

d) 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.

e) A perfectly rational poker-playing agent never loses.

A vacuum-cleaner world with just two locations. Each location can be clean or dirty, and the agent can move left or right and can clean the square that it occupies. Different versions of the vacuum world allow for different rules about what the agent can perceive, whether its actions always succeed, and so on