Consider the following premises. For all x_12, x_12 will work. For all x_12, x_12 will play a game if and only if x_12 is a nurse. For all x_12, x_12 will play a game or x_12 is an office clerk. For all x_12, x_12 is not a nurse. For all x_12, if x_12 were an office clerk, then x_12 is cooking. Can we infer the following from them? For all x_12, x_12 will cook and x_12 will work.
 From the fact that for all x_12, x_12 will play a game if and only if x_12 is a nurse, and that for all x_12, x_12 is not a nurse we can infer that for all x_12, x_12 will not play a game. From the fact that for all x_12, x_12 will play a game or x_12 is an office clerk, and that for all x_12, x_12 will not play a game we can infer that for all x_12, x_12 is an office clerk. From the fact that for all x_12, if x_12 were an office clerk, then x_12 is cooking, and that for all x_12, x_12 is an office clerk we can infer that for all x_12, x_12 will cook. Finally, from the fact that for all x_12, x_12 will cook, and that for all x_12, x_12 will work we can infer that for all x_12, x_12 will cook and x_12 will work. Therefore, the answer is yes.