Consider the following premises. If Joseph drives a car, then it is windy. If it is cloudy, then Joseph is driving a car. If it is windy, then Patricia is a janitor. If Patricia were a janitor, then it is cloudy. Can we infer the following from them? If is not true that Joseph is driving a car if and only if it is cloudy.
 From the fact that if Joseph drives a car, then it is windy, and that if it is windy, then Patricia is a janitor we can infer that if Joseph drives a car, then Patricia is a janitor. From the fact that if Joseph drives a car, then Patricia is a janitor, and that if Patricia were a janitor, then it is cloudy we can infer that if Joseph drives a car, then it is cloudy. Finally, from the fact that if Joseph drives a car, then it is cloudy, and that if it is cloudy, then Joseph is driving a car we can infer that Joseph is driving a car if and only if it is cloudy, which contradicts that If is not true that Joseph is driving a car if and only if it is cloudy. Therefore, the answer is no.