Consider the following premises. If Susan were sad, then Elisabeth is a scientist. If Elisabeth were a scientist, then Susan is sad. For all z, z is a police officer if and only if z is sad. Elisabeth is not a scientist. Can we infer the following from them? Susan is a police officer.
 From the fact that for all z, z is a police officer if and only if z is sad we can infer that Susan is a police officer if and only if Susan is sad. From the fact that if Elisabeth were a scientist, then Susan is sad, and that if Susan were sad, then Elisabeth is a scientist we can infer that Elisabeth is a scientist if and only if Susan is sad. From the fact that Elisabeth is a scientist if and only if Susan is sad, and that Elisabeth is not a scientist we can infer that Susan is not sad. Finally, from the fact that Susan is a police officer if and only if Susan is sad, and that Susan is not sad we can infer that Susan is not a police officer, which contradicts that Susan is a police officer. Therefore, the answer is no.