Symbolic Logic I Exercises in Constructing Conditional and ...



Symbolic Logic I Exercises in Constructing Conditional and Indirect Proofs

1) If you are ambitious, you'll never achieve all your goals. But life has meaning only if you have ambition. Thus, if you achieve all your goals, life has no meaning.(A, G, M,)

2) If Adam comes to the party, then Barbara will come, too. Furthermore, if Barbara comes to the party, so will Adam. So, Carlos will be happy if Adam comes only if Carlos will be happy if Barbara comes.(A, B, C)

3) If the president pursues arms limitations talks, then, if he gets the foreign policy mechanism working more harmoniously, the European left will acquiesce to the placement of additional nuclear weapons in Europe. But the European left will never acquiesce to that. So, either the president won't get the foreign policy mechanism working more harmoniously, or he won't pursue arms limitation talks.(P, F, A)

4) If we either introduce a new product line or give an existing line a new advertising image, then we'll be taking a risk, and we may lose market share. If we don't introduce a new product line, we won't have to make large expenditures on advertising. So, if we don't take risks, we won't have to make large expenditures on advertising.(I, G, R, L)

5) If we continue to run a large trade deficit, then the government will yield to calls for protectionism. We won't continue to run a large deficit only if our economy slows down or foreign economies recover. So, if foreign economies don't recover, then the government will resist calls for protectionism only if our economy slows down.(D, P, S, F)

6) Money either serves you or dominates you; never both. If it serves you, and you handle it wisely, then it can help you to attain happiness. If it dominates you, you will gain much of it, but never be satisfied with your lot. Moreover, you'll be satisfied with your lot if and only if money can't help you attain happiness. So, money can help you attain happiness if you handle it wisely.(S, D, W, H, G, L)

7) There will be scorpions in the house this week if there's any building going on in the neighborhood. There will be building if and only if the depression in the housing market ends. If there are scorpions in the house, the cats will kill them and bring them to me as trophies. Therefore, if the housing depression ends, my cats will bring me scorpions as trophies.(S, B, D, K, T)

8) If the president retaliates against Libya with military force, the public will be ambivalent. But if Libya directs terrorist attacks toward Americans on American soil, then the American public will not be ambivalent at all. So, Libya will not engage in terrorism against Americans on American soil unless the president doesn't retaliate militarily.(R, P, D)

9) If people don't either conserve energy or tolerate much greater despoiling of the environment, utilities will have no choice but to rely on nuclear power. They'll avoid relying on atomic energy, moreover, just in case it's prohibitively expensive and risky. Nuclear power will remain expensive. If it also remains risky, therefore, people will have to tolerate greater despoiling of the environment unless they conserve energy.(C, T, U, E, R)

10) If happiness can't be defined, there's no way to measure it. If we can't measure happiness, we can say whether someone is happy only if we take that person's word for it. Determining whether someone is happy is a necessary condition for testing the psychological effects of jobs of various kinds. We can't take a person's word concerning his or her own happiness. So, we can't test the psychological effects of various jobs if happiness can't be defined.

11) If Congress erects trade barriers and grants further subsidies to American farmers, then other countries will retaliate. If that happens, however, the economy will slow down; if there is a slowdown, then Congress won't give farmers additional subsidies unless it finds new sources of revenue. If Congress doesn't erect trade barriers, it won't give farmers added subsidies, but at least other countries won't retaliate. Therefore, unless Congress finds new revenue sources, farmers will get no additional subsidies from Congress.

12) If advertisers continue to use Saturday morning cartoons to peddle toys by creating shows about them, pressure for regulation will build, and ratings will decline if parents understand what's going on. If ratings decline, then advertisers will stop using cartoons to sell toys by having toys as their main characters. If pressure for regulation builds, then either advertisers will stop, or Congress will act. If Congress acts, then advertisers will stop. Hence, if advertisers continue, parents won't know what's going on, children will become obsessed with material goods, and American culture will irrevocably decline.

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