Consider the following premises. Joseph is not writing a letter. For all x_7, x_7 is curious if and only if x_7 will play a game. Joseph is writing a letter if and only if Patricia is playing a game. Can we infer the following from them? If we can, name the inference rule being used: Patricia is curious.
 From the fact that for all x_7, x_7 is curious if and only if x_7 will play a game we can infer that Patricia is curious if and only if Patricia is playing a game via universal instantiation. From the fact that Joseph is writing a letter if and only if Patricia is playing a game, and that Joseph is not writing a letter we can infer that Patricia is not playing a game via biconditional elimination. Finally, from the fact that Patricia is curious if and only if Patricia is playing a game, and that Patricia is not playing a game we can infer that Patricia is not curious via biconditional elimination, which contradicts that Patricia is curious. Therefore, the answer is no.