Consider the following premises. If it is overcast, then Sarah is a musician. If Sarah were a musician, then it is raining. It is not raining. If Linda climbs a mountain, then it is overcast. It is raining if and only if Linda is climbing a mountain. Can we infer the following from them? Sarah is not a musician.
 From the fact that it is raining if and only if Linda is climbing a mountain we can infer that if it rains, then Linda is climbing a mountain. From the fact that if Linda climbs a mountain, then it is overcast, and that if it is overcast, then Sarah is a musician we can infer that if Linda climbs a mountain, then Sarah is a musician. From the fact that if it rains, then Linda is climbing a mountain, and that if Linda climbs a mountain, then Sarah is a musician we can infer that if it rains, then Sarah is a musician. From the fact that if Sarah were a musician, then it is raining, and that if it rains, then Sarah is a musician we can infer that Sarah is a musician if and only if it is raining. Finally, from the fact that Sarah is a musician if and only if it is raining, and that it is not raining we can infer that Sarah is not a musician. Therefore, the answer is yes.