Consider the following premises. John is listening to a song or it is not snowing. John is listening to a song if and only if Elisabeth is a bartender. Can we infer the following from them? If we can, name the inference rule being used: The fact that it snows does not imply that Elisabeth is a bartender.
 From the fact that John is listening to a song if and only if Elisabeth is a bartender we can infer that if John listens to a song, then Elisabeth is a bartender via biconditional elimination. From the fact that John is listening to a song or it is not snowing we can infer that if it snows, then John is listening to a song via rewriting. Finally, from the fact that if it snows, then John is listening to a song, and that if John listens to a song, then Elisabeth is a bartender we can infer that if it snows, then Elisabeth is a bartender via transitivity, which contradicts that The fact that it snows does not imply that Elisabeth is a bartender. Therefore, the answer is no.