Consider the following premises. Richard is a cashier if and only if Sarah is an artist. Sarah is not an artist. If Charles plays tennis, then it is not raining. Richard is a cashier or it is raining. Can we infer the following from them? If we can, name the inference rule being used: Charles is not playing tennis.
 From the fact that Richard is a cashier if and only if Sarah is an artist, and that Sarah is not an artist we can infer that Richard is not a cashier via biconditional elimination. From the fact that Richard is a cashier or it is raining, and that Richard is not a cashier we can infer that it is raining via disjunctive syllogism. Finally, from the fact that if Charles plays tennis, then it is not raining, and that it is raining we can infer that Charles is not playing tennis via modus tollens. Therefore, the answer is yes.