Consider the following premises. Linda is not a sailor. If Sarah were a nurse, then Linda is a sailor. For all x_12, x_12 is sad if and only if x_12 is a nurse. It is cloudy if and only if Sarah is sad. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy.
 From the fact that for all x_12, x_12 is sad if and only if x_12 is a nurse we can infer that Sarah is sad if and only if Sarah is a nurse via universal instantiation. From the fact that if Sarah were a nurse, then Linda is a sailor, and that Linda is not a sailor we can infer that Sarah is not a nurse via modus tollens. From the fact that Sarah is sad if and only if Sarah is a nurse, and that Sarah is not a nurse we can infer that Sarah is not sad via biconditional elimination. Finally, from the fact that it is cloudy if and only if Sarah is sad, and that Sarah is not sad we can infer that it is not cloudy via biconditional elimination. Therefore, the answer is yes.