Chapter 6: Strategies and Derived Rules

1. Chapter 6: Strategies and Derived Rules 80-210: Logic & Proofs July 14, 2009 Karin Howe

2. Using Strategies Strategically • HAMMER!! first (&ER, &EL, E) • Is your goal the consequent of a conditional, but you don't have the antecedent available on other line? Apply E forwards to get the antecedent as a goal line. • Or-Out Strategy • Poof Variant on Or-Out Strategy • Backwards Strategy • Arrow-In Strategy • Reductio Strategy • Reductio Variant on Arrow-In Strategy

3. Derived Rules: One-Way Rules

4. Derived Rules: One-Way Rules

5. Derived Rules: One-Way Rules

6. Derived Rules: Two-Way Rules

7. A Smaller Bag of Tricks • Distribution: (Distr&, Distr&C, Distr, DistrC) • Disjunctive Syllogism: (DSR, DSL) • Modus Tollens: (MT) • Hypothetical Syllogism [Chain Argument]: (HS) • Exportation [Ham & Eggs]: (Exp&, Exp) • Definition of the Conditional and Negated Conditional [Arrow Rules]: (DefE, DefI, E, I) • DeMorgan's Laws: (DeM) • Transitivity [Contraposition]: (Trans) • Double Negation: (DNE, DNI)

8. Let's Practice! • Deriving the Derived Rules • Practice Problems • Lab