The Book ofFoundational Mathematics Detailed Contents Propositional Logic Propositions Modeling Logic with Truth Tables Logical Equivalence The Laws of Logic Application: Switching Networks Logical Implications Propositions with Variables Quantifiers Logic with Quantified Statements Nested Quantifiers Application: Logic Puzzles A Primer on Fuzzy Logic Mathematical Logic with Maple Defining Propositions with Maple Arguments and Proof The Structure of Basic 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 Verifying Mathematical Arguments in Maple Set Theory Sets Subsets Proof Technique: Element Arguments A Set of Operations on Sets The Laws of Set Theory Proof Technique: Exhaustion Russell’s Paradox and a Formal Resolution Set Theory in Maple 1 Propositional Logic Propositions Modeling Logic with Truth Tables Logical Equivalence The Laws of Logic Application: Switching Networks Logical Implications Propositions with Variables Quantifiers Logic with Quantified Statements Nested Quantifiers Application: Logic Puzzles A Primer on Fuzzy Logic Mathematical Logic With Maple Defining Propositions With Maple 2 Arguments and Proof The Structure of Basic 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 Verifying Mathematical Arguments in Maple 3 Set Theory Sets Subsets Proof Technique: Element Arguments A Set of Operations on Sets The Laws of Set Theory Proof Technique: Exhaustion Set Theory in Maple 4 Relations Appendix Further Reading