Consider the following premises. ~R_2(j_1). forall x_2: R_2(x_2) <-> S_2(x_2). Can we infer ~S_2(j_1) from them? If possible, name the inference rules being used at each step.
 From forall x_2: R_2(x_2) <-> S_2(x_2) we can infer R_2(j_1) <-> S_2(j_1) via universal instantiation. Finally, from R_2(j_1) <-> S_2(j_1), ~R_2(j_1) we can infer ~S_2(j_1) via biconditional elimination. Therefore, the answer is yes.