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