Symbolize each argument using the letters suggested. Construct formal deductions for the valid arguments below. Each of these can also be proven using the method of truth-trees.
- If the president of the university meets with the activists and he accepts their demands, then the diversity plan will be instituted. The president, in fact, accepts the demands. If the diversity plan is accepted, then both resources will be available and there will be no more protests. The president meets with the activists. Therefore, there will be no more protests. (P: The president meets with the activists. A: The president accepts the demands. D: The diversity plan will be accepted. R: Resources will be available. N: There will be protests.)
- Everyone can tell right from wrong. But if moral judgment is a personal matter, then there is no moral law. Of course, there is a moral law, if J. S. Mill was correct. If everyone can tell right from wrong, then Mill was correct. Therefore, moral judgment is not a personal matter. (E: Everyone can tell right from wrong. P: Moral judgment is a personal matter. L: There is a moral law. M: Mill was correct.)
- Cindy can go to the coast this weekend or she can stay at home; she cannot do both. If she wants to study, then she will need to stay home. If she wants to pass the class, then she wants to study. She definitely wants to pass the class. Therefore, she cannot go to the coast. (C: Cindy can go to the coast this weekend. H: Cindy can stay home this weekend. P: Cindy wants to pass. S: Cindy wants to study.)