Consider the following premises. For all x_26, x_26 is a nurse and x_26 is an astronaut. Joseph is writing a letter if and only if James is an artist. If Joseph writes a letter, then Sarah is not a nurse. Can we infer the following from them? James is not an artist or Patricia is cooking.
 From the fact that for all x_26, x_26 is a nurse and x_26 is an astronaut we can infer that for all x_26, x_26 is a nurse. From the fact that for all x_26, x_26 is a nurse we can infer that Sarah is a nurse. From the fact that if Joseph writes a letter, then Sarah is not a nurse, and that Sarah is a nurse we can infer that Joseph is not writing a letter. From the fact that Joseph is writing a letter if and only if James is an artist, and that Joseph is not writing a letter we can infer that James is not an artist. Finally, from the fact that James is not an artist we can infer that James is not an artist or Patricia is cooking. Therefore, the answer is yes.