Consider the following premises. Richard is a mechanic if and only if Karen is a server. John is working if and only if Richard is writing a letter. Karen is not a server. For all y, if y writes a letter, then y is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: John is working.
 From the fact that for all y, if y writes a letter, then y is a mechanic we can infer that if Richard writes a letter, then Richard is a mechanic via universal instantiation. From the fact that Richard is a mechanic if and only if Karen is a server, and that Karen is not a server we can infer that Richard is not a mechanic via biconditional elimination. From the fact that if Richard writes a letter, then Richard is a mechanic, and that Richard is not a mechanic we can infer that Richard is not writing a letter via modus tollens. Finally, from the fact that John is working if and only if Richard is writing a letter, and that Richard is not writing a letter we can infer that John is not working via biconditional elimination, which contradicts that John is working. Therefore, the answer is no.