Consider the following premises. Robert is making tea or Mary is not a politician. If Robert makes tea, then Michael is playing a game. Can we infer the following from them? The fact that Mary were a politician does not imply that Michael is playing a game.
 From the fact that Robert is making tea or Mary is not a politician we can infer that if Mary were a politician, then Robert is making tea. Finally, from the fact that if Mary were a politician, then Robert is making tea, and that if Robert makes tea, then Michael is playing a game we can infer that if Mary were a politician, then Michael is playing a game, which contradicts that The fact that Mary were a politician does not imply that Michael is playing a game. Therefore, the answer is no.