Consider the following premises. William is poor if and only if Patricia is writing a letter. If it is late, then William is poor. If William were poor, then it is late. If Patricia writes a letter, then William is poor. Patricia is not writing a letter. Can we infer the following from them? It is late.
 From the fact that William is poor if and only if Patricia is writing a letter we can infer that if William were poor, then Patricia is writing a letter. From the fact that if William were poor, then Patricia is writing a letter, and that if Patricia writes a letter, then William is poor we can infer that William is poor if and only if Patricia is writing a letter. From the fact that William is poor if and only if Patricia is writing a letter, and that Patricia is not writing a letter we can infer that William is not poor. From the fact that if William were poor, then it is late, and that if it is late, then William is poor we can infer that William is poor if and only if it is late. Finally, from the fact that William is poor if and only if it is late, and that William is not poor we can infer that it is not late, which contradicts that It is late. Therefore, the answer is no.