Consider the following premises. If it is cloudy, then Joseph is writing a letter. Joseph is not writing a letter. If Mary plays tennis, then it is cloudy. For all x_15, if x_15 were a police officer, then x_15 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: Mary is not a police officer.
 From the fact that for all x_15, if x_15 were a police officer, then x_15 is playing tennis we can infer that if Mary were a police officer, then Mary is playing tennis via universal instantiation. From the fact that if Mary were a police officer, then Mary is playing tennis, and that if Mary plays tennis, then it is cloudy we can infer that if Mary were a police officer, then it is cloudy via transitivity. From the fact that if it is cloudy, then Joseph is writing a letter, and that Joseph is not writing a letter we can infer that it is not cloudy via modus tollens. Finally, from the fact that if Mary were a police officer, then it is cloudy, and that it is not cloudy we can infer that Mary is not a police officer via modus tollens. Therefore, the answer is yes.