Consider the following premises. John is a mechanic if and only if James is playing a game. Mary is cooking if and only if James is playing a game. Mary is not cooking. If it is sunny, then John is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: It is sunny.
 From the fact that Mary is cooking if and only if James is playing a game, and that Mary is not cooking we can infer that James is not playing a game via biconditional elimination. From the fact that John is a mechanic if and only if James is playing a game, and that James is not playing a game we can infer that John is not a mechanic via biconditional elimination. Finally, from the fact that if it is sunny, then John is a mechanic, and that John is not a mechanic we can infer that it is not sunny via modus tollens, which contradicts that It is sunny. Therefore, the answer is no.