Consider the following premises. exists x_2: P_2(x_2) -> Q_2(x_2). forall x_2: P_2(x_2). forall x_2: S_2(x_2). Can we infer exists x_2: S_2(x_2) and Q_2(x_2) from them? If possible, name the inference rules being used at each step.
 From exists x_2: P_2(x_2) -> Q_2(x_2), forall x_2: P_2(x_2) we can infer exists x_2: Q_2(x_2) via existential modus ponens. Finally, from forall x_2: S_2(x_2), exists x_2: Q_2(x_2) we can infer exists x_2: S_2(x_2) and Q_2(x_2) via existential conjunction. Therefore, the answer is yes.