Chapter 8: Statement Logic: Proofs

8.1 Introduces the method of natural deduction and provides eight implicational inference rules: modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, constructive dilemma, simplification, conjunction, and addition.

8.2. Adds five equivalence rules to the system of natural deduction: double-negation, commutation, association, De Morgan's laws, and contraposition.

8.3 Adds five more equivalence rules to the system of natural deduction: distribution, exportation, redundancy, material equivalence, and material implication.

8.4 Adds Conditional Proof to the system of natural deduction.

8.5 Adds Reductio ad Absurdum to the system of natural deduction.

8.6 Explains what a theorem is and how to construct proofs for theorems. Also introduces the concept of a corresponding conditional for an argument, and explains why the corresponding conditional of a valid argument in statement logic is always a theorem.