Consider the following premises. Jessica is a janitor or Jessica is not a carpenter. For all x_1, if x_1 were a janitor, then x_1 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Jessica is a carpenter if and only if Jessica is a janitor.
 From the fact that for all x_1, if x_1 were a janitor, then x_1 is a carpenter we can infer that if Jessica were a janitor, then Jessica is a carpenter via universal instantiation. From the fact that Jessica is a janitor or Jessica is not a carpenter we can infer that if Jessica were a carpenter, then Jessica is a janitor via rewriting. Finally, from the fact that if Jessica were a carpenter, then Jessica is a janitor, and that if Jessica were a janitor, then Jessica is a carpenter we can infer that Jessica is a carpenter if and only if Jessica is a janitor via biconditional introduction, which contradicts that If is not true that Jessica is a carpenter if and only if Jessica is a janitor. Therefore, the answer is no.