1. (20 pts.) True/False (a) (2) True/False: There exist task environments E1 and E2 and agent A such that A is perfectly rational in both E1 and E2, even though E1 and E2 are not identical. (b) (2) True/False: Search algorithms cannot be applied in completely unobservable environments (c) (2) True/False: Every existentially quantified sentence in first-order logic is true in any model that contains exactly one object. (d) (2) True/False: A perfectly rational backgammon agent never loses. (e) (2) True/False: Depth-first search always expands at least as many nodes as A search with an admissible heuristic. (f) (2) True/False: There exists a task environment (PEAS) in which every agent is rational. (g) (2) True/False: Suppose agent A selects its action uniformly at random from the set of possible actions. There exists a deterministic, fully observable task environment in which A is rational. (h) (2) True/False: No logical agent can behave rationally in partially observable environment (i) (2) True/False: PA -P is satisfiable. (i) (2) True/False: Two clauses can be used to deduce a new clause using resolution, so long as they each contain one of a pair of complementary literals