1 / 9

Strategies and Derived Rules in Logic: Enhancing Proof Techniques

This chapter delves into advanced strategies and derived rules for logical reasoning and proofs. It introduces techniques such as the Hammer strategy, the Or-Out strategy, and several other strategic approaches (e.g., Backwards Strategy, Reductio) that facilitate logical deductions. The section on derived rules includes discussions on one-way and two-way rules such as Distribution, Disjunctive Syllogism, Modus Tollens, and DeMorgan’s Laws. The chapter concludes with practice problems designed to strengthen your command of these derived rules and logical strategies, enabling deeper understanding and application in proofs.

sol
Télécharger la présentation

Strategies and Derived Rules in Logic: Enhancing Proof Techniques

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related