Consider the following premises. For all x_10, if x_10 listens to a song, then x_10 is curious. For all x_10, x_10 is a carpenter. For all x_10, x_10 is curious if and only if x_10 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is curious or x_10 is rich.
 From the fact that for all x_10, x_10 is curious if and only if x_10 is a carpenter we can infer that for all x_10, if x_10 were a carpenter, then x_10 is curious via universal biconditional elimination. From the fact that for all x_10, x_10 is a carpenter we can infer that for all x_10, x_10 is a carpenter or x_10 will listen to a song via universal addition. From the fact that for all x_10, if x_10 were a carpenter, then x_10 is curious, that for all x_10, if x_10 listens to a song, then x_10 is curious, and that for all x_10, x_10 is a carpenter or x_10 will listen to a song we can infer that for all x_10, x_10 is curious via universal disjunction elimination. Finally, from the fact that for all x_10, x_10 is curious we can infer that for all x_10, x_10 is curious or x_10 is rich via universal addition. Therefore, the answer is yes.