Consider the following premises. For all x, x will go running if and only if x will play a game. For all x, x will not drink water. For all x, if x plays a game, then x is drinking water. For all x, x will go running if and only if x is a writer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is a writer.
 From the fact that for all x, if x plays a game, then x is drinking water, and that for all x, x will not drink water we can infer that for all x, x will not play a game via universal modus tollens. From the fact that for all x, x will go running if and only if x will play a game, and that for all x, x will not play a game we can infer that for all x, x will not go running via universal biconditional elimination. Finally, from the fact that for all x, x will go running if and only if x is a writer, and that for all x, x will not go running we can infer that for all x, x is not a writer via universal biconditional elimination, which contradicts that There is at least one x for which x is a writer. Therefore, the answer is no.