Consider the following premises. For all z, z will climb a mountain if and only if z will write a letter. It is cloudy. Mary is not climbing a mountain. Can we infer the following from them? It is cloudy and Mary is not writing a letter.
 From the fact that for all z, z will climb a mountain if and only if z will write a letter we can infer that Mary is climbing a mountain if and only if Mary is writing a letter. From the fact that Mary is climbing a mountain if and only if Mary is writing a letter, and that Mary is not climbing a mountain we can infer that Mary is not writing a letter. Finally, from the fact that it is cloudy, and that Mary is not writing a letter we can infer that it is cloudy and Mary is not writing a letter. Therefore, the answer is yes.