Consider the following premises. Mary is a carpenter if and only if Jennifer is a police officer. For all x_8, x_8 is a police officer or x_8 is a politician. Mary is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not a politician.
 From the fact that for all x_8, x_8 is a police officer or x_8 is a politician we can infer that Jennifer is a police officer or Jennifer is a politician via universal instantiation. From the fact that Mary is a carpenter if and only if Jennifer is a police officer, and that Mary is not a carpenter we can infer that Jennifer is not a police officer via biconditional elimination. Finally, from the fact that Jennifer is a police officer or Jennifer is a politician, and that Jennifer is not a police officer we can infer that Jennifer is a politician via disjunctive syllogism, which contradicts that Jennifer is not a politician. Therefore, the answer is no.