Consider the following premises. If Barbara writes a letter, then Jessica is a mechanic. If Charles were a janitor, then Patricia is a carpenter. Charles is a janitor or Jessica is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: The fact that Barbara writes a letter does not imply that Patricia is a carpenter.
 From the fact that Charles is a janitor or Jessica is not a mechanic we can infer that if Jessica were a mechanic, then Charles is a janitor via rewriting. From the fact that if Barbara writes a letter, then Jessica is a mechanic, and that if Jessica were a mechanic, then Charles is a janitor we can infer that if Barbara writes a letter, then Charles is a janitor via transitivity. Finally, from the fact that if Barbara writes a letter, then Charles is a janitor, and that if Charles were a janitor, then Patricia is a carpenter we can infer that if Barbara writes a letter, then Patricia is a carpenter via transitivity, which contradicts that The fact that Barbara writes a letter does not imply that Patricia is a carpenter. Therefore, the answer is no.