Chapter 1 Reasoning and Proof

1.1 Axiomatic Development of Mathematics

1.1.1 Undefined Terms

1.1.2 Undefined Relations

1.1.3 Axioms Relating the Undefined Terms and Undefined Relations

1.1.4 Theorems

1.2 Logic and Propositional Calculus

1.2.1 Propositions and Compound Propositions

1.3 Reasoning

1.3.1 Inductive Reasoning

1.3.2 Deductive Reasoning

1.4 Logical Operations

1.4.1 Conditional Statements

1.4.2 Basic Logical Operations

1.4.3 Propositions and Truth Tables

1.4.4 Tautologies and Contradictions

1.4.5 Logical Equivalence

1.4.6 Algebra of Propositions

1.4.7 Conditional and Biconditional Statements

1.4.8 Arguments

1.4.9 Logical Implication

1.5 Sets and Basic Operations on Sets

1.5.1 Introduction

1.5.2 Sets and Elements

1.5.3 Universal Set, Empty Set

1.5.4 Subsets

1.5.5 Venn Diagrams

1.5.6 Set Operations

1.5.7 Algebra of Sets

1.5.8 Finite Sets, Counting Principles

1.5.9 Classes of Sets, Power Sets

1.5.10 Arguments and Venn Diagrams

1.6 Reason Using Properties of Algebra