Consider the following premises. If Linda writes a letter, then Elisabeth is an astronaut. For all z, z is not an astronaut. If Patricia were a politician, then Linda is writing a letter. Can we infer the following from them? Patricia is not a politician.
 From the fact that for all z, z is not an astronaut we can infer that Elisabeth is not an astronaut. From the fact that if Linda writes a letter, then Elisabeth is an astronaut, and that Elisabeth is not an astronaut we can infer that Linda is not writing a letter. Finally, from the fact that if Patricia were a politician, then Linda is writing a letter, and that Linda is not writing a letter we can infer that Patricia is not a politician. Therefore, the answer is yes.