Consider the following premises. It is not cold. Mary is not a poet. If Elisabeth writes a letter, then it is cold. Mary is a poet if and only if Robert is playing a game. Can we infer the following from them? If we can, name the inference rule being used: Robert is playing a game.
 From the fact that if Elisabeth writes a letter, then it is cold, and that it is not cold we can infer that Elisabeth is not writing a letter via modus tollens. Finally, from the fact that Mary is a poet if and only if Robert is playing a game, and that Mary is not a poet we can infer that Robert is not playing a game via biconditional elimination, which contradicts that Robert is playing a game. Therefore, the answer is no.