Consider the following premises. p_2 or ~t. p_2 -> t. Can we infer ~(p_2 <-> t) from them?
 From p_2 or ~t we can infer t -> p_2. Finally, from p_2 -> t, t -> p_2 we can infer p_2 <-> t, which contradicts ~(p_2 <-> t). Therefore, the answer is no.