Consider the following premises. If it is cloudy, then James is a musician. Robert is an astronaut if and only if it is cloudy. If James were a musician, then Robert is an astronaut. Can we infer the following from them? If is not true that it is cloudy if and only if Robert is an astronaut.
 From the fact that Robert is an astronaut if and only if it is cloudy we can infer that if Robert were an astronaut, then it is cloudy. From the fact that if it is cloudy, then James is a musician, and that if James were a musician, then Robert is an astronaut we can infer that if it is cloudy, then Robert is an astronaut. Finally, from the fact that if it is cloudy, then Robert is an astronaut, and that if Robert were an astronaut, then it is cloudy we can infer that it is cloudy if and only if Robert is an astronaut, which contradicts that If is not true that it is cloudy if and only if Robert is an astronaut. Therefore, the answer is no.