Consider the following premises. P_1(j). forall z_4: R_2(z_4). Can we infer exists z_4: P_1(z_4) and R_2(z_4) from them? If possible, name the inference rules being used at each step.
 From P_1(j) we can infer exists z_4: P_1(z_4) via existential generalization. Finally, from exists z_4: P_1(z_4), forall z_4: R_2(z_4) we can infer exists z_4: P_1(z_4) and R_2(z_4) via existential conjunction. Therefore, the answer is yes.