Consider the following premises. forall x_21: R_21(x_21) <-> S_21(x_21). ~p_3. R_21(a_21) <-> p_3. Can we infer ~S_21(a_21) or u from them? If possible, name the inference rules being used at each step.
 From forall x_21: R_21(x_21) <-> S_21(x_21) we can infer R_21(a_21) <-> S_21(a_21) via universal instantiation. From R_21(a_21) <-> p_3 we can infer R_21(a_21) -> p_3 via biconditional elimination. From R_21(a_21) -> p_3, ~p_3 we can infer ~R_21(a_21) via modus tollens. From R_21(a_21) <-> S_21(a_21), ~R_21(a_21) we can infer ~S_21(a_21) via biconditional elimination. Finally, from ~S_21(a_21) we can infer ~S_21(a_21) or u via addition. Therefore, the answer is yes.