Consider the following premises. For all x_12, x_12 is an astronaut if and only if x_12 is a carpenter. William is taking a plane or Jessica is not an astronaut. Can we infer the following from them? If Jessica were a carpenter, then William is taking a plane.
 From the fact that for all x_12, x_12 is an astronaut if and only if x_12 is a carpenter we can infer that Jessica is an astronaut if and only if Jessica is a carpenter. From the fact that Jessica is an astronaut if and only if Jessica is a carpenter we can infer that if Jessica were a carpenter, then Jessica is an astronaut. From the fact that William is taking a plane or Jessica is not an astronaut we can infer that if Jessica were an astronaut, then William is taking a plane. Finally, from the fact that if Jessica were a carpenter, then Jessica is an astronaut, and that if Jessica were an astronaut, then William is taking a plane we can infer that if Jessica were a carpenter, then William is taking a plane. Therefore, the answer is yes.