Consider the following premises. Jessica is sad if and only if Elisabeth is a poet. Jessica is not sad. If Elisabeth were not a poet, then James is a bartender. Can we infer the following from them? If we can, name the inference rule being used: James is not a bartender.
 From the fact that Jessica is sad if and only if Elisabeth is a poet, and that Jessica is not sad we can infer that Elisabeth is not a poet via biconditional elimination. Finally, from the fact that if Elisabeth were not a poet, then James is a bartender, and that Elisabeth is not a poet we can infer that James is a bartender via modus ponens, which contradicts that James is not a bartender. Therefore, the answer is no.