Consider the following premises. q_1 <-> q_3. s_3. q_1 -> q_4. q_3 -> ~s_3. q_1 or ~q_4. Can we infer ~q_4 from them? If possible, name the inference rules being used at each step.
 From q_3 -> ~s_3, s_3 we can infer ~q_3 via modus tollens. From q_1 <-> q_3, ~q_3 we can infer ~q_1 via biconditional elimination. From q_1 or ~q_4 we can infer q_4 -> q_1 via rewriting. From q_1 -> q_4, q_4 -> q_1 we can infer q_1 <-> q_4 via biconditional introduction. Finally, from q_1 <-> q_4, ~q_1 we can infer ~q_4 via biconditional elimination. Therefore, the answer is yes.