B$)$ For the following statements, explain if it's True or False:

The danger of depth$-$first search is that it may not terminate if the search space is infinite, even if a finite solution exists.

TF

Agent is a function without infrastructure.

TF

Heuristics are needed to define a structure to an algorithm.

TF

C$]$ 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$)$ The input to an agent program is the same as the input to the agent function.

c$)$ A perfectly rational poker$-$playing agent never loses.