Consider the following premises. u. ~s_4. s_4 <-> r. r or q_4. Can we infer ~q_4 from them? If possible, name the inference rules being used at each step.
 From s_4 <-> r, ~s_4 we can infer ~r via biconditional elimination. Finally, from r or q_4, ~r we can infer q_4 via disjunctive syllogism, which contradicts ~q_4. Therefore, the answer is no.