Consider the following premises. p_3 -> q. p_10 -> r_2. ~r_2. p_10 or p_3. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From p_10 -> r_2, ~r_2 we can infer ~p_10 via modus tollens. From p_10 or p_3, ~p_10 we can infer p_3 via disjunctive syllogism. Finally, from p_3 -> q, p_3 we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.