Consider the following premises. If Mary listens to a song, then Michael is writing a letter. It is sunny if and only if Michael is writing a letter. If Michael writes a letter, then Mary is listening to a song. Mary is not listening to a song. Can we infer the following from them? It is sunny.
 From the fact that if Mary listens to a song, then Michael is writing a letter, and that if Michael writes a letter, then Mary is listening to a song we can infer that Mary is listening to a song if and only if Michael is writing a letter. From the fact that Mary is listening to a song if and only if Michael is writing a letter, and that Mary is not listening to a song we can infer that Michael is not writing a letter. Finally, from the fact that it is sunny if and only if Michael is writing a letter, and that Michael is not writing a letter we can infer that it is not sunny, which contradicts that It is sunny. Therefore, the answer is no.