Consider the following premises. For all x_5, if x_5 were a carpenter, then x_5 is a politician. If Charles were a politician, then Charles is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Charles is a carpenter if and only if Charles is a politician.
 From the fact that for all x_5, if x_5 were a carpenter, then x_5 is a politician we can infer that if Charles were a carpenter, then Charles is a politician via universal instantiation. Finally, from the fact that if Charles were a carpenter, then Charles is a politician, and that if Charles were a politician, then Charles is a carpenter we can infer that Charles is a carpenter if and only if Charles is a politician via biconditional introduction, which contradicts that If is not true that Charles is a carpenter if and only if Charles is a politician. Therefore, the answer is no.