Consider the following premises. For all x_6, x_6 will play squash. For all x_6, if x_6 plays squash, then x_6 is cooking. For all x_6, if x_6 were a politician, then x_6 is cooking. Can we infer the following from them? There is at least one x for which x will cook.
 From the fact that for all x_6, x_6 will play squash we can infer that for all x_6, x_6 will play squash or x_6 is a politician. From the fact that for all x_6, if x_6 plays squash, then x_6 is cooking, that for all x_6, if x_6 were a politician, then x_6 is cooking, and that for all x_6, x_6 will play squash or x_6 is a politician we can infer that for all x_6, x_6 will cook. From the fact that for all x_6, x_6 will cook we can infer that Karen is cooking. Finally, from the fact that Karen is cooking we can infer that there is at least one x for which x will cook. Therefore, the answer is yes.