1. If high-tech products are exported to Russia, then domestic industries will benefit. If the Russians can effectively utilize high-tech products, then their standard of living will improve. Therefore, if high-tech products are exported to Russia and the Russians can effectively utilize them, then their standard of living will improve and domestic industries will benefit. (H, D, U, S)

2. 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, I, W, S)

3. A doctor must disconnect a dying patient from a respirator if and only if the fact that patients are self-determining implies that the doctor must follow the patient's orders. If a dying patient refuses treatment, then the doctor must disconnect the patient from a respirator and the patient will die peacefully. Patients are self-determining. Therefore, if a dying patient refuses treatment, then the doctor must follow the patient's orders. (D, S, F, R, P)

4. If jails are overcrowded, then dangerous suspects will be released on their own recognizance. If jails are overcrowded and dangerous suspects are released on their own recognizance, then crime will increase. If no new jails are built and crime increases, then innocent victims will pay the price of increased crime. Therefore, if jails are overcrowded, then if no new jails are built, then innocent victims will pay the price of increased crime. (J, D, C, N, I)

5. If astronauts attempt interplanetary space travel, then heavy shielding will be required to protect them from solar radiation. If massive amounts of either fuel or water are carried, then the spacecraft must be very large. Therefore, if heavy shielding is required to protect the astronauts from solar radiation only if massive amounts of fuel are carried, then if astronauts attempt interplanetary space travel, then the spacecraft must be very large. (A, H, F, W, L)

Translate the following arguments into symbolic form, using the letters in the order in which they are listed. Then use conditional proof and the eighteen rules of inference to derive the conclusion of each. Having done so, attempt to derive the conclusion without using conditional proof.