Introduction to Logic: Lessons

• Introduction to Logic
• Semantics for Sentential Logic (Truth Tables)
• Syntax of Sentential Logic; Parentheses
• Derivations, Rules of Inference, Validity
• Working Premises, Dependencies, and Conditional Proof
• Further Rules of Inference
• New and Derived Rules of Inference
• Further Rules of Indirect Proof Procedure
• Validity, Counterexample, Tautology
• Integer Arithmetic
• Two Rules About Equality
• More Rules About Equality
• The Replace Equals Rules
• Practive Using Equality in Integer Arithmetic
• The Commutative Axiom for Integer Arithmetic
• The Associative Axiom
• Two Axioms and a Definition for Commutative Groups
• Theorems 1-3 for Commutative Groups
• Theorems 4-7 for Commutative Groups
• Noncommutative Groups
• Finding Axioms Exercises
• Symbolizing Sentential Arguments
• Symbolizing English Sentences in Predicate Logic
• Inferences Involving Quantifiers
• Quantifiers; Restrictions and Derived Rules
• Using Interpretations to Show Arguments Invalid
• Quantifiers and Interpretation
• Consistency of Premises and Independence of Axioms
• The Logic of Identity (and Sorted Theories)