Consider the following premises. forall y: U(y) or Q_2(y). forall y: ~R(y). forall y: R(y) <-> U(y). Can we infer ~Q_2(a) from them? If possible, name the inference rules being used at each step.
 From forall y: R(y) <-> U(y), forall y: ~R(y) we can infer forall y: ~U(y) via universal biconditional elimination. Finally, from forall y: U(y) or Q_2(y), forall y: ~U(y) we can infer forall y: Q_2(y) via universal disjunctive syllogism, which contradicts ~Q_2(a). Therefore, the answer is no.