Consider the following premises. For all x_11, x_11 is a scientist if and only if x_11 will cook. David is not cooking. Can we infer the following from them? David is not a scientist or it is raining.
 From the fact that for all x_11, x_11 is a scientist if and only if x_11 will cook we can infer that David is a scientist if and only if David is cooking. From the fact that David is a scientist if and only if David is cooking, and that David is not cooking we can infer that David is not a scientist. Finally, from the fact that David is not a scientist we can infer that David is not a scientist or it is raining. Therefore, the answer is yes.