Consider the following premises. For all x_21, if x_21 were a writer, then x_21 is listening to a song. For all x_21, x_21 will drink water or x_21 is a writer. For all x_21, x_21 will listen to a song if and only if x_21 is fast. For all x_21, if x_21 drinks water, then x_21 is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: William is not fast.
 From the fact that for all x_21, if x_21 drinks water, then x_21 is listening to a song, that for all x_21, if x_21 were a writer, then x_21 is listening to a song, and that for all x_21, x_21 will drink water or x_21 is a writer we can infer that for all x_21, x_21 will listen to a song via universal disjunction elimination. From the fact that for all x_21, x_21 will listen to a song if and only if x_21 is fast we can infer that for all x_21, if x_21 listens to a song, then x_21 is fast via universal biconditional elimination. Finally, from the fact that for all x_21, if x_21 listens to a song, then x_21 is fast, and that for all x_21, x_21 will listen to a song we can infer that for all x_21, x_21 is fast via universal modus ponens, which contradicts that William is not fast. Therefore, the answer is no.