Consider the following premises. Jessica is not a soldier. Jessica is cooking if and only if Patricia is a politician. For all x_8, if x_8 were a soldier, then x_8 is cooking. For all x_8, if x_8 cooks, then x_8 is a soldier. Can we infer the following from them? Patricia is a politician.
 From the fact that for all x_8, if x_8 were a soldier, then x_8 is cooking, and that for all x_8, if x_8 cooks, then x_8 is a soldier we can infer that for all x_8, x_8 is a soldier if and only if x_8 will cook. From the fact that for all x_8, x_8 is a soldier if and only if x_8 will cook we can infer that Jessica is a soldier if and only if Jessica is cooking. From the fact that Jessica is a soldier if and only if Jessica is cooking, and that Jessica is not a soldier we can infer that Jessica is not cooking. Finally, from the fact that Jessica is cooking if and only if Patricia is a politician, and that Jessica is not cooking we can infer that Patricia is not a politician, which contradicts that Patricia is a politician. Therefore, the answer is no.