Consider the following premises. u_4 <-> p_3. u_4. p_3 -> p_4. Can we infer ~p_4 from them? If possible, name the inference rules being used at each step.
 From u_4 <-> p_3 we can infer u_4 -> p_3 via biconditional elimination. From u_4 -> p_3, u_4 we can infer p_3 via modus ponens. Finally, from p_3 -> p_4, p_3 we can infer p_4 via modus ponens, which contradicts ~p_4. Therefore, the answer is no.