Consider the following premises. forall x_4: W(x_4). exists x_4: Q_4(x_4). forall x_4: W(x_4) <-> U_2(x_4). Can we infer exists x_4: Q_4(x_4) and U_2(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: W(x_4) <-> U_2(x_4) we can infer forall x_4: W(x_4) -> U_2(x_4) via universal biconditional elimination. From forall x_4: W(x_4) -> U_2(x_4), forall x_4: W(x_4) we can infer forall x_4: U_2(x_4) via universal modus ponens. Finally, from exists x_4: Q_4(x_4), forall x_4: U_2(x_4) we can infer exists x_4: Q_4(x_4) and U_2(x_4) via existential conjunction. Therefore, the answer is yes.