Consider the following premises. If Joseph were an astronaut, then Patricia is an office clerk. Joseph is not working. If Patricia were an office clerk, then Joseph is an astronaut. Joseph is working if and only if Joseph is an astronaut. Can we infer the following from them? Patricia is not an office clerk.
 From the fact that Joseph is working if and only if Joseph is an astronaut, and that Joseph is not working we can infer that Joseph is not an astronaut. From the fact that if Joseph were an astronaut, then Patricia is an office clerk, and that if Patricia were an office clerk, then Joseph is an astronaut we can infer that Joseph is an astronaut if and only if Patricia is an office clerk. Finally, from the fact that Joseph is an astronaut if and only if Patricia is an office clerk, and that Joseph is not an astronaut we can infer that Patricia is not an office clerk. Therefore, the answer is yes.