Consider the following premises. If Charles were an astronaut, then Elisabeth is a cashier. Elisabeth is not a cashier. Patricia is a police officer if and only if Charles is an astronaut. Can we infer the following from them? Patricia is not a police officer.
 From the fact that if Charles were an astronaut, then Elisabeth is a cashier, and that Elisabeth is not a cashier we can infer that Charles is not an astronaut. Finally, from the fact that Patricia is a police officer if and only if Charles is an astronaut, and that Charles is not an astronaut we can infer that Patricia is not a police officer. Therefore, the answer is yes.