Consider the following premises. If Jessica were a lawyer, then it is cloudy. If Jessica were a lawyer, then Susan is a musician. It is not cloudy. If Susan were a musician, then it is cold. Jessica is a lawyer if and only if it is cold. Can we infer the following from them? It is not cold.
 From the fact that Jessica is a lawyer if and only if it is cold we can infer that if it is cold, then Jessica is a lawyer. From the fact that if Jessica were a lawyer, then Susan is a musician, and that if Susan were a musician, then it is cold we can infer that if Jessica were a lawyer, then it is cold. From the fact that if it is cold, then Jessica is a lawyer, and that if Jessica were a lawyer, then it is cold we can infer that it is cold if and only if Jessica is a lawyer. From the fact that if Jessica were a lawyer, then it is cloudy, and that it is not cloudy we can infer that Jessica is not a lawyer. Finally, from the fact that it is cold if and only if Jessica is a lawyer, and that Jessica is not a lawyer we can infer that it is not cold. Therefore, the answer is yes.