Consider the following premises. It is overcast if and only if Elisabeth is a writer. Elisabeth is a writer or it is not overcast. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is overcast does not imply that Elisabeth is a writer.
 From the fact that it is overcast if and only if Elisabeth is a writer we can infer that if Elisabeth were a writer, then it is overcast via biconditional elimination. Finally, from the fact that Elisabeth is a writer or it is not overcast we can infer that if it is overcast, then Elisabeth is a writer via rewriting, which contradicts that The fact that it is overcast does not imply that Elisabeth is a writer. Therefore, the answer is no.