**Logic **

Statements, Negation, and Compound Statements

Truth Tables and Logical Equivalences

Conditional and Biconditional Statements

Logical Arguments

Open Statements and Quantifiers

**Deductive Mathematical Systems and Proofs**

Deductive Mathematical Systems

Mathematical Proofs

**Set Theory**

Sets and Subsets

Set Operations

Additional Set Operations

Generalized Set Union and Intersection

**Relations **

Relations

The Order Relations <, =, >, =

Reflexive, Symmetric, Transitive, and Equivalence Relations

Equivalence Relations, Equivalence Classes, and Partitions

**Functions **

Functions

Onto Functions, One-to-One Functions, and One-to-One Correspondences

Inverse of a Function

Images and Inverse Images of Sets

**Mathematical Induction**

Mathematical Induction

The Well-Ordering Principle and the Fundamental Theorem of Arithmetic

**Cardinalities of Sets**

Finite Sets

Denumerable and Countable Sets

Uncountable Sets

**Proofs from Real Analysis**

Sequences

Limit Theorems for Sequences

Monotone Sequences and Subsequences

Cauchy Sequences

**Proofs from Group Theory**

Binary Operations and Algebraic Structures

Groups

Subgroups and Cyclic Groups

**Appendix: Reading and Writing Mathematical Proofs**

**Answers to Selected Exercises **

**References **

**Index**