Problem:
Translate the following argument into symbolic form using the translation key given in parentheses. Then use conditional proof and the eighteen rules of inference to derive the conclusions of the symbolized argument below.
If the police take you into custody, then if they inform you that you have the right to remain silent, then whatever you say will be used against you. If the police inform you that you have the right to remain silent, then if whatever you say will be used against you, then you should not say anything. Therefore, if the police take you into custody, then if they inform you that you have the right to remain silent, then you should not say anything. (P = The police take you into custody. I = The police inform you that you have the right to remain silent. W = Whatever you say will be used against you. S = You should say something.)