Consider the following premises. For all x_21, x_21 is a cashier if and only if x_21 will play a game. For all x_21, x_21 will read a book or x_21 is a sailor. For all x_21, if x_21 were a sailor, then x_21 is a cashier. For all x_21, if x_21 reads a book, then x_21 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not playing a game.
 From the fact that for all x_21, if x_21 reads a book, then x_21 is a cashier, that for all x_21, if x_21 were a sailor, then x_21 is a cashier, and that for all x_21, x_21 will read a book or x_21 is a sailor we can infer that for all x_21, x_21 is a cashier via universal disjunction elimination. From the fact that for all x_21, x_21 is a cashier if and only if x_21 will play a game we can infer that for all x_21, if x_21 were a cashier, then x_21 is playing a game via universal biconditional elimination. Finally, from the fact that for all x_21, if x_21 were a cashier, then x_21 is playing a game, and that for all x_21, x_21 is a cashier we can infer that for all x_21, x_21 will play a game via universal modus ponens, which contradicts that Patricia is not playing a game. Therefore, the answer is no.