Consider the following premises. If Michael were a mechanic, then David is playing a game. Michael is a mechanic or David is not playing a game. Michael is a mechanic if and only if David is playing a game. Can we infer the following from them? If is not true that David is playing a game if and only if Michael is a mechanic.
 From the fact that Michael is a mechanic or David is not playing a game we can infer that if David plays a game, then Michael is a mechanic. Finally, from the fact that if David plays a game, then Michael is a mechanic, and that if Michael were a mechanic, then David is playing a game we can infer that David is playing a game if and only if Michael is a mechanic, which contradicts that If is not true that David is playing a game if and only if Michael is a mechanic. Therefore, the answer is no.