Consider the following premises. If Patricia were an astronaut, then Elisabeth is poor. If Elisabeth were poor, then Patricia is an astronaut. If it is windy, then Patricia is an astronaut. It is windy or Elisabeth is poor. Can we infer the following from them? Patricia is an astronaut.
 From the fact that if Elisabeth were poor, then Patricia is an astronaut, and that if Patricia were an astronaut, then Elisabeth is poor we can infer that Elisabeth is poor if and only if Patricia is an astronaut. From the fact that Elisabeth is poor if and only if Patricia is an astronaut we can infer that if Elisabeth were poor, then Patricia is an astronaut. Finally, from the fact that if it is windy, then Patricia is an astronaut, that if Elisabeth were poor, then Patricia is an astronaut, and that it is windy or Elisabeth is poor we can infer that Patricia is an astronaut. Therefore, the answer is yes.