Consider the following premises. For all x_8, x_8 will cook if and only if x_8 is a musician. Elisabeth is not a musician. Can we infer the following from them? Elisabeth is not cooking.
 From the fact that for all x_8, x_8 will cook if and only if x_8 is a musician we can infer that for all x_8, if x_8 cooks, then x_8 is a musician. From the fact that for all x_8, if x_8 cooks, then x_8 is a musician we can infer that if Elisabeth cooks, then Elisabeth is a musician. Finally, from the fact that if Elisabeth cooks, then Elisabeth is a musician, and that Elisabeth is not a musician we can infer that Elisabeth is not cooking. Therefore, the answer is yes.