Consider the following premises. It is overcast if and only if it is cloudy. If Jessica were sad, then Richard is a nurse. Richard is a nurse if and only if it is cloudy. It is not overcast. Can we infer the following from them? If we can, name the inference rule being used: Jessica is sad.
 From the fact that it is overcast if and only if it is cloudy, and that it is not overcast we can infer that it is not cloudy via biconditional elimination. From the fact that Richard is a nurse if and only if it is cloudy, and that it is not cloudy we can infer that Richard is not a nurse via biconditional elimination. Finally, from the fact that if Jessica were sad, then Richard is a nurse, and that Richard is not a nurse we can infer that Jessica is not sad via modus tollens, which contradicts that Jessica is sad. Therefore, the answer is no.