Consider the following premises. Elisabeth is not a politician. Robert is making tea if and only if it is raining. If it doesn't rain, then Jessica is running. Elisabeth is a politician if and only if Robert is making tea. Can we infer the following from them? If we can, name the inference rule being used: Jessica is running.
 From the fact that Elisabeth is a politician if and only if Robert is making tea we can infer that if Robert makes tea, then Elisabeth is a politician via biconditional elimination. From the fact that if Robert makes tea, then Elisabeth is a politician, and that Elisabeth is not a politician we can infer that Robert is not making tea via modus tollens. From the fact that Robert is making tea if and only if it is raining, and that Robert is not making tea we can infer that it is not raining via biconditional elimination. Finally, from the fact that if it doesn't rain, then Jessica is running, and that it is not raining we can infer that Jessica is running via modus ponens. Therefore, the answer is yes.