Consider the following premises. If it is cloudy, then Linda is an office clerk. It is cloudy or Karen is a police officer. Joseph is a scientist if and only if Karen is a police officer. If Joseph were a scientist, then Linda is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: Linda is not an office clerk.
 From the fact that Joseph is a scientist if and only if Karen is a police officer we can infer that if Karen were a police officer, then Joseph is a scientist via biconditional elimination. From the fact that if Karen were a police officer, then Joseph is a scientist, and that if Joseph were a scientist, then Linda is an office clerk we can infer that if Karen were a police officer, then Linda is an office clerk via transitivity. Finally, from the fact that if it is cloudy, then Linda is an office clerk, that if Karen were a police officer, then Linda is an office clerk, and that it is cloudy or Karen is a police officer we can infer that Linda is an office clerk via disjunction elimination, which contradicts that Linda is not an office clerk. Therefore, the answer is no.