Consider the following premises. David is a bartender. If it is sunny, then Elisabeth is a carpenter. If Elisabeth were a carpenter, then David is not a bartender. It is sunny or Robert is cooking. Can we infer the following from them? If we can, name the inference rule being used: Robert is not cooking.
 From the fact that if Elisabeth were a carpenter, then David is not a bartender, and that David is a bartender we can infer that Elisabeth is not a carpenter via modus tollens. From the fact that if it is sunny, then Elisabeth is a carpenter, and that Elisabeth is not a carpenter we can infer that it is not sunny via modus tollens. Finally, from the fact that it is sunny or Robert is cooking, and that it is not sunny we can infer that Robert is cooking via disjunctive syllogism, which contradicts that Robert is not cooking. Therefore, the answer is no.