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The Book of Foundational Mathematics Foundational Mathematics
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      • Foundational Mathematics
        • Table of Contents
        • 1. Logic
          • Propositions
          • Modeling Logic with Truth Tables
          • Logical Order of Operations
          • Satisfiability
          • Laws of Logic
          • Simplifying Logical Expressions
          • Application: Switching Networks
          • Open Propositions
          • Quantifiers
          • Quantified Laws of Logic
          • Multiple Quantifiers
          • Application: Modeling Logic Puzzles
        • 2. Proof
          • A Closer Look at the Implication
          • Variations on the Implication
          • Logical Implications
          • Quantified Logical Implications
          • Arguments
          • Rules of Inference
          • Using the Rules of Inference
          • Logically Equivalent Arguments
          • Invalid Arguments
          • Universal Specification
          • Universal Generalization
          • Axioms, Definitions, Theorems, and Proofs
          • Proof Technique: Direct Proofs
          • Proof Technique: Indirect Proofs
          • Proof Technique: Contradiction
          • Mistakes in Proofs
          • Proof Technique: Equivalence
        • 3. Set Theory
          • Sets
          • Size of a Set
          • Subsets
          • The Empty Set
          • Proof Technique: Element Arguments
          • A Set of Operations on Sets
          • Graphical Depictions of Sets
          • The Laws of Set Theory
          • Proof Technique: Exhaustion
          • Set Partitions
          • Proof Technique: Casework
          • Russell's Paradox and a Formal Resolution
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