Chapter One: Logic and Introduction to Proofs
1.1: Propositional Logic
- Constructing Compound Propositions
- Negation
- Conjunction
- Disjunction
- Implication
- Biconditional
- Truth Tables
Chapter 1.1
1.2: Application of Propositional Logic
- Translating Propositional Logic Statements
- Translating English Sentences
Chapter 1.2
1.3: Propositional Equivalences
- Proving Logical Equivalences with Truth Tables
- Tautology, contradiction, contingency
- Logical Equivalences including De Morgan’s Law
Chapter 1.3
1.4: Predicates and Quantifiers
- Predicate Logic
- Propositional Functions
- Quantifiers
- Negating the Translating with Quantifiers
- Propositonal Functions Examples
Chapter 1.4
1.5: Nested Quantifiers
- Translating with Nested Quantifiers
Chapter 1.5
1.6: Rules of Interence
- Different Rules of Inference
Chapter 1.6
1.7: Introduction to Proofs
- Direct Proof
- Contraposition
Chapter 1.7
1.8: Proof Methods and Strategy
Chapter 1.8
