1. If government deficits continue at their present rate and a recession sets in, then interest on the national debt will become unbearable and the government will default on its loans. If a recession sets in, then the government will not default on its loans. Therefore, either government deficits will not continue at their present rate or a recession will not set in. (C, R, I, D)

2. If either the sea turtle population continues to decrease or rescue efforts are commenced to save the sea turtle from extinction, then nesting sanctuaries will be created and the indiscriminate slaughter of these animals will be halted. If either nesting sanctuaries are created or poachers are arrested, then if the indiscriminate slaughter of these animals is halted, then the sea turtle population will not continue to decrease. Therefore, the sea turtle population will not continue to decrease. (C, R, N, I, P)

3. If asbestos workers sue their employers, then if punitive damages are awarded, then their employers will declare bankruptcy. If asbestos workers sue their employers, then punitive damages will be awarded. If asbestos workers contract asbestosis, then either they will sue their employers or their employers will declare bankruptcy. Therefore, either asbestos workers will not contract asbestosis or their employers will declare bankruptcy. (S, P, B, C)

4. If astronauts spend long periods in zero gravity only if calcium is resorbed in their bodies, then astronauts on a Mars voyage will arrive with brittle bones. If astronauts attempt a voyage to Mars only if they spend long periods in zero gravity, then astronauts on a Mars voyage will arrive with brittle bones. Therefore, astronauts on a Mars voyage will arrive with brittle bones. (Z, C, B, V)

5. Either deposits should be required on beer and soft-drink containers, or these containers will be discarded along highways and the countryside will look like a dump. If these containers will be discarded either in parks or along highways, then deposits should be required on soft-drink containers. Therefore, deposits should be required on soft-drink containers. (B, S, H, C, P)

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