Consider the following premises. For all x, x will listen to a song. For all x, x will make tea. There is at least one x for which x is rich. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is rich and x will listen to a song.
 From the fact that for all x, x will listen to a song, and that for all x, x will make tea we can infer that for all x, x will listen to a song and x will make tea via universal conjunction. From the fact that for all x, x will listen to a song and x will make tea we can infer that for all x, x will listen to a song via universal simplification. Finally, from the fact that there is at least one x for which x is rich, and that for all x, x will listen to a song we can infer that there is at least one x for which x is rich and x will listen to a song via existential conjunction. Therefore, the answer is yes.