Consider the following premises. exists x: S(x) -> W_2(x). forall x: W_2(x) <-> Q_2(x). Can we infer exists x: S(x) -> Q_2(x) from them?
 From forall x: W_2(x) <-> Q_2(x) we can infer forall x: W_2(x) -> Q_2(x). Finally, from exists x: S(x) -> W_2(x), forall x: W_2(x) -> Q_2(x) we can infer exists x: S(x) -> Q_2(x). Therefore, the answer is yes.