Consider the following premises. If Sarah cooks, then Jessica is listening to a song. It is late or Jessica is not listening to a song. Sarah is a doctor if and only if it is late. Sarah is a doctor or Sarah is cooking. Can we infer the following from them? It is not late.
 From the fact that it is late or Jessica is not listening to a song we can infer that if Jessica listens to a song, then it is late. From the fact that if Sarah cooks, then Jessica is listening to a song, and that if Jessica listens to a song, then it is late we can infer that if Sarah cooks, then it is late. From the fact that Sarah is a doctor if and only if it is late we can infer that if Sarah were a doctor, then it is late. Finally, from the fact that if Sarah were a doctor, then it is late, that if Sarah cooks, then it is late, and that Sarah is a doctor or Sarah is cooking we can infer that it is late, which contradicts that It is not late. Therefore, the answer is no.