Consider the following premises. If Thomas were sad, then it is snowing. It is overcast if and only if Elisabeth is cooking. If it snows, then it is overcast. Thomas is sad or Elisabeth is cooking. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that it is overcast if and only if Elisabeth is cooking we can infer that if Elisabeth cooks, then it is overcast via biconditional elimination. From the fact that if Thomas were sad, then it is snowing, and that if it snows, then it is overcast we can infer that if Thomas were sad, then it is overcast via transitivity. Finally, from the fact that if Thomas were sad, then it is overcast, that if Elisabeth cooks, then it is overcast, and that Thomas is sad or Elisabeth is cooking we can infer that it is overcast via disjunction elimination, which contradicts that It is not overcast. Therefore, the answer is no.