Consider the following premises. w. forall x_4: P(x_4) -> Q_4(x_4). p_6 -> Q_4(j_4). p_6 or P(j_4). Can we infer Q_4(j_4) and w from them? If possible, name the inference rules being used at each step.
 From forall x_4: P(x_4) -> Q_4(x_4) we can infer P(j_4) -> Q_4(j_4) via universal instantiation. From p_6 -> Q_4(j_4), P(j_4) -> Q_4(j_4), p_6 or P(j_4) we can infer Q_4(j_4) via disjunction elimination. Finally, from Q_4(j_4), w we can infer Q_4(j_4) and w via conjunction. Therefore, the answer is yes.