Consider the following premises. It is late. Elisabeth is sad if and only if Elisabeth is not running. Elisabeth is running if and only if Elisabeth is a nurse. Elisabeth is not a nurse. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is sad and it is late.
 From the fact that Elisabeth is running if and only if Elisabeth is a nurse, and that Elisabeth is not a nurse we can infer that Elisabeth is not running via biconditional elimination. From the fact that Elisabeth is sad if and only if Elisabeth is not running we can infer that if Elisabeth doesn't go running, then Elisabeth is sad via biconditional elimination. From the fact that if Elisabeth doesn't go running, then Elisabeth is sad, and that Elisabeth is not running we can infer that Elisabeth is sad via modus ponens. Finally, from the fact that Elisabeth is sad, and that it is late we can infer that Elisabeth is sad and it is late via conjunction. Therefore, the answer is yes.