Consider the following premises. Elisabeth is a nurse and it is overcast. Joseph is an electrician or Elisabeth is not a nurse. Can we infer the following from them? If we can, name the inference rule being used: Joseph is an electrician.
 From the fact that Elisabeth is a nurse and it is overcast we can infer that Elisabeth is a nurse via simplification. From the fact that Joseph is an electrician or Elisabeth is not a nurse we can infer that if Elisabeth were a nurse, then Joseph is an electrician via rewriting. Finally, from the fact that if Elisabeth were a nurse, then Joseph is an electrician, and that Elisabeth is a nurse we can infer that Joseph is an electrician via modus ponens. Therefore, the answer is yes.