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