Consider the following premises. If Patricia were a bartender, then David is a scientist. James is listening to a song or it is not snowing. If David were a scientist, then it is snowing. Can we infer the following from them? The fact that Patricia were a bartender does not imply that James is listening to a song.
 From the fact that if Patricia were a bartender, then David is a scientist, and that if David were a scientist, then it is snowing we can infer that if Patricia were a bartender, then it is snowing. From the fact that James is listening to a song or it is not snowing we can infer that if it snows, then James is listening to a song. Finally, from the fact that if Patricia were a bartender, then it is snowing, and that if it snows, then James is listening to a song we can infer that if Patricia were a bartender, then James is listening to a song, which contradicts that The fact that Patricia were a bartender does not imply that James is listening to a song. Therefore, the answer is no.