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