Consider the following premises. Sarah is not playing tennis. If William were a cashier, then Patricia is driving a car. Patricia is driving a car if and only if Sarah is playing tennis. If Patricia drives a car, then William is a cashier. Can we infer the following from them? William is not a cashier.
 From the fact that Patricia is driving a car if and only if Sarah is playing tennis, and that Sarah is not playing tennis we can infer that Patricia is not driving a car. From the fact that if William were a cashier, then Patricia is driving a car, and that if Patricia drives a car, then William is a cashier we can infer that William is a cashier if and only if Patricia is driving a car. Finally, from the fact that William is a cashier if and only if Patricia is driving a car, and that Patricia is not driving a car we can infer that William is not a cashier. Therefore, the answer is yes.