Consider the following premises. For all x_8, if x_8 drinks water, then x_8 is a musician. For all x_8, if x_8 were a musician, then x_8 is drinking water. William is not drinking water. If it rains, then William is a musician. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that for all x_8, if x_8 were a musician, then x_8 is drinking water, and that for all x_8, if x_8 drinks water, then x_8 is a musician we can infer that for all x_8, x_8 is a musician if and only if x_8 will drink water via universal biconditional introduction. From the fact that for all x_8, x_8 is a musician if and only if x_8 will drink water we can infer that William is a musician if and only if William is drinking water via universal instantiation. From the fact that William is a musician if and only if William is drinking water, and that William is not drinking water we can infer that William is not a musician via biconditional elimination. Finally, from the fact that if it rains, then William is a musician, and that William is not a musician we can infer that it is not raining via modus tollens. Therefore, the answer is yes.