Consider the following premises. t_4 -> q_3. w -> t_4. u <-> w. Can we infer ~(u -> q_3) from them? If possible, name the inference rules being used at each step.
 From w -> t_4, t_4 -> q_3 we can infer w -> q_3 via transitivity. From u <-> w we can infer u -> w via biconditional elimination. Finally, from u -> w, w -> q_3 we can infer u -> q_3 via transitivity, which contradicts ~(u -> q_3). Therefore, the answer is no.