Consider the following premises. For all y_4, if y_4 were an artist, then y_4 is a doctor. Patricia is a lawyer. For all y_4, if y_4 were a doctor, then y_4 is an artist. Linda is not a doctor. Can we infer the following from them? Patricia is a lawyer and Linda is not an artist.
 From the fact that for all y_4, if y_4 were a doctor, then y_4 is an artist, and that for all y_4, if y_4 were an artist, then y_4 is a doctor we can infer that for all y_4, y_4 is a doctor if and only if y_4 is an artist. From the fact that for all y_4, y_4 is a doctor if and only if y_4 is an artist we can infer that Linda is a doctor if and only if Linda is an artist. From the fact that Linda is a doctor if and only if Linda is an artist, and that Linda is not a doctor we can infer that Linda is not an artist. Finally, from the fact that Patricia is a lawyer, and that Linda is not an artist we can infer that Patricia is a lawyer and Linda is not an artist. Therefore, the answer is yes.