Consider the following premises. exists z_1: P(z_1) -> R(z_1). forall z_1: W(z_1). forall z_1: P(z_1). Can we infer exists z_1: R(z_1) and W(z_1) from them? If possible, name the inference rules being used at each step.
 From exists z_1: P(z_1) -> R(z_1), forall z_1: P(z_1) we can infer exists z_1: R(z_1) via existential modus ponens. Finally, from exists z_1: R(z_1), forall z_1: W(z_1) we can infer exists z_1: R(z_1) and W(z_1) via existential conjunction. Therefore, the answer is yes.