Consider the following premises. If Jennifer were a politician, then it is raining. If it is cloudy, then Charles is a writer. If Charles were a writer, then Jennifer is a politician. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is cloudy does not imply that it is raining.
 From the fact that if Charles were a writer, then Jennifer is a politician, and that if Jennifer were a politician, then it is raining we can infer that if Charles were a writer, then it is raining via transitivity. Finally, from the fact that if it is cloudy, then Charles is a writer, and that if Charles were a writer, then it is raining we can infer that if it is cloudy, then it is raining via transitivity, which contradicts that The fact that it is cloudy does not imply that it is raining. Therefore, the answer is no.