Consider the following premises. Elisabeth is a cashier or Michael is not sleeping. If Elisabeth were a cashier, then Linda is a musician. Linda is not a musician. Can we infer the following from them? If we can, name the inference rule being used: Michael is sleeping.
 From the fact that if Elisabeth were a cashier, then Linda is a musician, and that Linda is not a musician we can infer that Elisabeth is not a cashier via modus tollens. From the fact that Elisabeth is a cashier or Michael is not sleeping we can infer that if Michael sleeps, then Elisabeth is a cashier via rewriting. Finally, from the fact that if Michael sleeps, then Elisabeth is a cashier, and that Elisabeth is not a cashier we can infer that Michael is not sleeping via modus tollens, which contradicts that Michael is sleeping. Therefore, the answer is no.