Relationships in Truth Statements
Read sections 2.9 through 2.13 (pages 90–113) to learn more about relationships among truth statements and using and constructing logical proofs.
Section 2.9 reviews materially equivalent propositions. Section 2.10 reviews three other relationships among statements: tautological relationships, contradictory relationships, and contingent relationships. Section 2.11 reviews the eight valid forms of inference: 1. modus ponens, 2. modus tollens, 3. hypothetical syllogism, 4. simplification, 5. conjunction, 6. disjunctive syllogism, 7. addition, and 8. constructive dilemma. Section 2.12 reviews constructing proofs, including strategies for working forward or backward, depending on which is easier according to your premises. Finally, section 2.13 summarizes everything you have learned about sentential and propositional logic.
Complete exercises 14, 15, 16, and 17 as you study. Check your answers against the answer keys on pages 217-224.