Consider the following premises. exists x: W(x) or ~Q(x). forall x: Q(x) or ~W(x). Can we infer exists x: Q(x) <-> W(x) from them? If possible, name the inference rules being used at each step.
 From forall x: Q(x) or ~W(x) we can infer forall x: W(x) -> Q(x) via universal rewriting. From exists x: W(x) or ~Q(x) we can infer exists x: Q(x) -> W(x) via existential rewriting. Finally, from exists x: Q(x) -> W(x), forall x: W(x) -> Q(x) we can infer exists x: Q(x) <-> W(x) via existential biconditional introduction. Therefore, the answer is yes.