Consider the following premises. w_1 -> p. p_2 -> s. p -> p_2. ~s. Can we infer ~w_1 from them? If possible, name the inference rules being used at each step.
 From w_1 -> p, p -> p_2 we can infer w_1 -> p_2 via transitivity. From w_1 -> p_2, p_2 -> s we can infer w_1 -> s via transitivity. Finally, from w_1 -> s, ~s we can infer ~w_1 via modus tollens. Therefore, the answer is yes.