Consider the following premises. Joseph is a politician if and only if Sarah is a sailor. Jessica is not happy. If Joseph were a politician, then Jessica is happy. If Jessica were happy, then Joseph is a politician. Can we infer the following from them? Sarah is not a sailor or it is late.
 From the fact that if Jessica were happy, then Joseph is a politician, and that if Joseph were a politician, then Jessica is happy we can infer that Jessica is happy if and only if Joseph is a politician. From the fact that Jessica is happy if and only if Joseph is a politician, and that Jessica is not happy we can infer that Joseph is not a politician. From the fact that Joseph is a politician if and only if Sarah is a sailor, and that Joseph is not a politician we can infer that Sarah is not a sailor. Finally, from the fact that Sarah is not a sailor we can infer that Sarah is not a sailor or it is late. Therefore, the answer is yes.