Consider the following premises. If Sarah were a bartender, then it is cold. It is not cold. Sarah is a bartender or Richard is an electrician. It is cold if and only if Sarah is a bartender. Can we infer the following from them? If we can, name the inference rule being used: Richard is not an electrician.
 From the fact that it is cold if and only if Sarah is a bartender we can infer that if it is cold, then Sarah is a bartender via biconditional elimination. From the fact that if it is cold, then Sarah is a bartender, and that if Sarah were a bartender, then it is cold we can infer that it is cold if and only if Sarah is a bartender via biconditional introduction. From the fact that it is cold if and only if Sarah is a bartender, and that it is not cold we can infer that Sarah is not a bartender via biconditional elimination. Finally, from the fact that Sarah is a bartender or Richard is an electrician, and that Sarah is not a bartender we can infer that Richard is an electrician via disjunctive syllogism, which contradicts that Richard is not an electrician. Therefore, the answer is no.