Consider the following premises. If it is cold, then it is cloudy. It is cold. It is cloudy if and only if Karen is cooking. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy.
 From the fact that it is cold we can infer that it is cold or Karen is cooking via addition. From the fact that it is cloudy if and only if Karen is cooking we can infer that if Karen cooks, then it is cloudy via biconditional elimination. Finally, from the fact that if it is cold, then it is cloudy, that if Karen cooks, then it is cloudy, and that it is cold or Karen is cooking we can infer that it is cloudy via disjunction elimination, which contradicts that It is not cloudy. Therefore, the answer is no.