Discrete Mathematics..

viContents3.3 Operations on Sets 853.4 Counting Techniques 943.5 The Algebra of Sets 983.6 Families of Sets 1053.7 The Cartesian Product 1163.8 Types and Typed Set Theory 128Chapter 4: Relations 1484.1 Relations and Their Representations 1484.2 Properties of Relations 1584.3 Intersections and Unions of Relations 1654.4 Equivalence Relations and Partitions 1694.5 Order Relations 1824.6 Hasse Diagrams 1924.7 Application: Relational Databases 199Chapter 5: Functions 2145.1 Definitions and Examples 2145.2 Composite Functions 2325.3 Injections and Surjections 2405.4 Bijections and Inverse Functions 2545.5 More on Cardinality 2645.6 Databases: Functional Dependence and Normal Forms 271Chapter 6: Matrix Algebra 2856.1 Introduction 2856.2 Some Special Matrices 2886.3 Operations on Matrices 2906.4 Elementary Matrices 3026.5 The Inverse of a Matrix 312Chapter 7: Systems of Linear Equations 3257.1 Introduction 3257.2 Matrix Inverse Method 3317.3 Gauss–Jordan Elimination 3367.4 Gaussian Elimination 349Chapter 8: Algebraic Structures 3558.1 Binary Operations and their Properties 3558.2 Algebraic Structures 3648.3 More about Groups 3738.4 Some Families of Groups 3788.5 Substructures 3908.6 Morphisms 3988.7 Group Codes 412