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