Consider the following premises. For all x_15, if x_15 were a sailor, then x_15 is a musician. If it is overcast, then Karen is a musician. If Karen were a sailor, then it is overcast. For all x_15, if x_15 were a musician, then x_15 is a sailor. Can we infer the following from them? Karen is a musician if and only if it is overcast.
 From the fact that for all x_15, if x_15 were a sailor, then x_15 is a musician, and that for all x_15, if x_15 were a musician, then x_15 is a sailor we can infer that for all x_15, x_15 is a sailor if and only if x_15 is a musician. From the fact that for all x_15, x_15 is a sailor if and only if x_15 is a musician we can infer that for all x_15, if x_15 were a musician, then x_15 is a sailor. From the fact that for all x_15, if x_15 were a musician, then x_15 is a sailor we can infer that if Karen were a musician, then Karen is a sailor. From the fact that if Karen were a musician, then Karen is a sailor, and that if Karen were a sailor, then it is overcast we can infer that if Karen were a musician, then it is overcast. Finally, from the fact that if Karen were a musician, then it is overcast, and that if it is overcast, then Karen is a musician we can infer that Karen is a musician if and only if it is overcast. Therefore, the answer is yes.