Consider the following premises. It is not sunny. If Joseph were a poet, then James is writing a letter. Joseph is a poet if and only if Robert is an astronaut. James is writing a letter if and only if it is sunny. Can we infer the following from them? If we can, name the inference rule being used: Robert is not an astronaut.
 From the fact that Joseph is a poet if and only if Robert is an astronaut we can infer that if Robert were an astronaut, then Joseph is a poet via biconditional elimination. From the fact that James is writing a letter if and only if it is sunny, and that it is not sunny we can infer that James is not writing a letter via biconditional elimination. From the fact that if Joseph were a poet, then James is writing a letter, and that James is not writing a letter we can infer that Joseph is not a poet via modus tollens. Finally, from the fact that if Robert were an astronaut, then Joseph is a poet, and that Joseph is not a poet we can infer that Robert is not an astronaut via modus tollens. Therefore, the answer is yes.