Consider the following premises. Jennifer is a server if and only if William is writing a letter. Jennifer is not a server. It is overcast. If it is overcast, then William is writing a letter. If William writes a letter, then it is overcast. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that if William writes a letter, then it is overcast, and that if it is overcast, then William is writing a letter we can infer that William is writing a letter if and only if it is overcast via biconditional introduction. From the fact that Jennifer is a server if and only if William is writing a letter, and that Jennifer is not a server we can infer that William is not writing a letter via biconditional elimination. From the fact that William is writing a letter if and only if it is overcast, and that William is not writing a letter we can infer that it is not overcast via biconditional elimination. From the fact that it is overcast we can infer that it is overcast or it is cold via addition. Finally, from the fact that it is overcast or it is cold, and that it is not overcast we can infer that it is cold via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.