Consider the following premises. Joseph is making tea. Joseph is making tea if and only if Susan is a writer. Can we infer the following from them? If we can, name the inference rule being used: Susan is not a writer.
 From the fact that Joseph is making tea if and only if Susan is a writer we can infer that if Joseph makes tea, then Susan is a writer via biconditional elimination. Finally, from the fact that if Joseph makes tea, then Susan is a writer, and that Joseph is making tea we can infer that Susan is a writer via modus ponens, which contradicts that Susan is not a writer. Therefore, the answer is no.