Consider the following premises. If it is sunny, then James is a politician. If it is sunny, then Jennifer is writing a letter. If James were a politician, then it is sunny. If Jennifer writes a letter, then James is a politician. Can we infer the following from them? If is not true that Jennifer is writing a letter if and only if it is sunny.
 From the fact that if it is sunny, then James is a politician, and that if James were a politician, then it is sunny we can infer that it is sunny if and only if James is a politician. From the fact that it is sunny if and only if James is a politician we can infer that if James were a politician, then it is sunny. From the fact that if Jennifer writes a letter, then James is a politician, and that if James were a politician, then it is sunny we can infer that if Jennifer writes a letter, then it is sunny. Finally, from the fact that if Jennifer writes a letter, then it is sunny, and that if it is sunny, then Jennifer is writing a letter we can infer that Jennifer is writing a letter if and only if it is sunny, which contradicts that If is not true that Jennifer is writing a letter if and only if it is sunny. Therefore, the answer is no.