Consider the following premises. For all x_12, if x_12 were a scientist, then x_12 is an astronaut. Elisabeth is a scientist or Elisabeth is not an astronaut. Can we infer the following from them? If Elisabeth were an astronaut, then Elisabeth is a scientist.
 From the fact that for all x_12, if x_12 were a scientist, then x_12 is an astronaut we can infer that if Elisabeth were a scientist, then Elisabeth is an astronaut. Finally, from the fact that Elisabeth is a scientist or Elisabeth is not an astronaut we can infer that if Elisabeth were an astronaut, then Elisabeth is a scientist. Therefore, the answer is yes.