Consider the following premises. It is overcast if and only if John is a lawyer. It is overcast. John is not a lawyer. Can we infer the following from them? If we can, name the inference rule being used: Michael is a nurse.
 From the fact that it is overcast we can infer that it is overcast or Michael is a nurse via addition. From the fact that it is overcast if and only if John is a lawyer, and that John is not a lawyer we can infer that it is not overcast via biconditional elimination. Finally, from the fact that it is overcast or Michael is a nurse, and that it is not overcast we can infer that Michael is a nurse via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.