Suppose a logic-based agent in the wumpus world has found that locations (1,1) and (2,1) do not contain a stench, but that locations (3,1) and (2,2) do contain a stench. Can the agent deduce the location of the wumpus? Let's use propositional logic to find out.

a. Using propositional symbols Sx,y for stench in (x,y) and Wx,y for wumpus in (x,y), where x and y are integers greater than zero, write down a knowledge base containing relevant propositional statements about the wumpus world and containing what the agent knows about this wumpus world. Number each statement.

b. Show a propositional proof of the location of the wumpus. For each step of your proof, clearly indicate the newly inferred statement, the previous statements used to infer this new statement, and the inference rule used.