These lectures cover introductory sentential logic, a method used to draw inferences based off of an argument’s premises. Sentential logic (also known as propositional calculus) is an integral part of discrete math, set theory, computer programming, law, philosophy, game theory, and all other proof-based disciplines. This course begins with basic logical operators before moving to truth tables, replacement rules, inference rules, and proof strategies.
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The Beginning
- Introduction
- Overview
Simple Sentences and Operations
- Finding Simple Sentences
- Representing Simple Sentences
- Negation
- OR/Disjunction
- Compound Sentences
- AND/Conjunction
- Conditional (IF-THEN) Statements
- Biconditional (IF AND ONLY IF)
Truth Tables
- Truth Tables Introduction
- Truth Table Practice
- Why Are “Vacuously True” Statements True?
- Exclusive OR
- Complicated Truth Tables
Replacement Rules
- Double Negation
- Material Implication
- Contraposition
- DeMorgan’s Law, Part 1
- DeMorgan’s Law, Part 2
- Applying Replacement Rules
- Associativity
- Commutativity
- Hard Replacement Rule Problem
- Distribution
- Idempotence
Rules of Inference
- Modus Ponens
- Modus Tollens
- Disjunctive Syllogism
- Hypothetical Syllogism
- Constructive Dilemma
- Destructive Dilemma
- Conjunction Introduction
- Simplification
- Biconditional Introduction and Elimination
- Disjunction Introduction
Proofs
- Introduction to Proofs
- Killer Proof Strategy #1: DeMorgan’s Everything!
- Killer Proof Strategy #2: Work Backward
- Proof by Contradiction/Indirect Proof
- Conditional Proofs
- Tautologies
- Nested Proofs
- Proof Practices #1, #2, and #3
- Killer Proof Strategy #3: Proof by Cases
- Biconditional Tautologies
Formal Fallacies