Consider the following premises. James is listening to a song or William is making tea. If William makes tea, then James is drinking water. It is not cold. If Joseph were a carpenter, then James is not drinking water. It is cold or Charles is sad. For all x_32, if x_32 listens to a song, then x_32 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: Charles is sad and Joseph is not a carpenter.
 From the fact that for all x_32, if x_32 listens to a song, then x_32 is drinking water we can infer that if James listens to a song, then James is drinking water via universal instantiation. From the fact that if James listens to a song, then James is drinking water, that if William makes tea, then James is drinking water, and that James is listening to a song or William is making tea we can infer that James is drinking water via disjunction elimination. From the fact that if Joseph were a carpenter, then James is not drinking water, and that James is drinking water we can infer that Joseph is not a carpenter via modus tollens. From the fact that it is cold or Charles is sad, and that it is not cold we can infer that Charles is sad via disjunctive syllogism. Finally, from the fact that Charles is sad, and that Joseph is not a carpenter we can infer that Charles is sad and Joseph is not a carpenter via conjunction. Therefore, the answer is yes.