Consider the following premises. Thomas is not listening to a song. If Joseph were a writer, then Jessica is a poet. If Jessica were a poet, then Thomas is listening to a song. Joseph is a writer if and only if it is late. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that if Jessica were a poet, then Thomas is listening to a song, and that Thomas is not listening to a song we can infer that Jessica is not a poet via modus tollens. From the fact that Joseph is a writer if and only if it is late we can infer that if it is late, then Joseph is a writer via biconditional elimination. From the fact that if Joseph were a writer, then Jessica is a poet, and that Jessica is not a poet we can infer that Joseph is not a writer via modus tollens. Finally, from the fact that if it is late, then Joseph is a writer, and that Joseph is not a writer we can infer that it is not late via modus tollens, which contradicts that It is late. Therefore, the answer is no.