Consider the following premises. Michael is a poet if and only if it is sunny. Michael is a poet if and only if Richard is writing a letter. Richard is not writing a letter. Can we infer the following from them? If we can, name the inference rule being used: It is sunny.
 From the fact that Michael is a poet if and only if Richard is writing a letter we can infer that if Michael were a poet, then Richard is writing a letter via biconditional elimination. From the fact that if Michael were a poet, then Richard is writing a letter, and that Richard is not writing a letter we can infer that Michael is not a poet via modus tollens. Finally, from the fact that Michael is a poet if and only if it is sunny, and that Michael is not a poet we can infer that it is not sunny via biconditional elimination, which contradicts that It is sunny. Therefore, the answer is no.