Consider the following premises. For all x, x is a janitor if and only if x will write a letter. If Jessica were a janitor, then Jessica is writing a letter. Jessica is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: Jessica is writing a letter.
 From the fact that for all x, x is a janitor if and only if x will write a letter we can infer that for all x, if x writes a letter, then x is a janitor via universal biconditional elimination. From the fact that for all x, if x writes a letter, then x is a janitor we can infer that if Jessica writes a letter, then Jessica is a janitor via universal instantiation. From the fact that if Jessica writes a letter, then Jessica is a janitor, and that if Jessica were a janitor, then Jessica is writing a letter we can infer that Jessica is writing a letter if and only if Jessica is a janitor via biconditional introduction. Finally, from the fact that Jessica is writing a letter if and only if Jessica is a janitor, and that Jessica is not a janitor we can infer that Jessica is not writing a letter via biconditional elimination, which contradicts that Jessica is writing a letter. Therefore, the answer is no.