$2\mathrm{.}3$ Let us examine the rationality of various vaccum$-$cleaner agent functions.

a$.$ Show that the simple vaccum$-$cleaner agent function described in Figure $2\mathrm{.}3$ is indeed rational inder the assumptions listed on Page $38$

b$.$ Describe a rational agent Function for the case in which each movement costs one point. Does the corresponding agent program require internal state?

c$.$ Discuss possible agent designs for the cases in which clean squares cna become dirty and the geography of the enciorment