Consider the following premises. forall y: P(y) -> Q(y). forall y: W(y) -> P(y). exists y: W(y) or ~Q(y). Can we infer exists y: W(y) <-> Q(y) from them?
 From forall y: W(y) -> P(y), forall y: P(y) -> Q(y) we can infer forall y: W(y) -> Q(y). From exists y: W(y) or ~Q(y) we can infer exists y: Q(y) -> W(y). Finally, from forall y: W(y) -> Q(y), exists y: Q(y) -> W(y) we can infer exists y: W(y) <-> Q(y). Therefore, the answer is yes.