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Section 8.0 8.0.1

Chapter 8Relations

8.1 Relations and Their Properties

8.2* n-ary Relations

8.3 Representing Relations

8.4 Closures of Relations

8.5 Equivalence Relations

8.6 Partial Orderings

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.1 Relations & Their Properties 8.1.1

8.1 RELATIONS & THEIR PROPERTIES

CONCEPTUALIZATION and MODELING

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.1.2 Chapter 8 Relations

MORE EXAMPLES

GENERALIZATION

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.1 Relations & Their Properties 8.1.3

ALTERNATIVE MODELS of RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.1.4 Chapter 8 Relations

COMPOSITION OF BINARY RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.1 Relations & Their Properties 8.1.5

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.1.6 Chapter 8 Relations

REFLEXIVE PROPERTY of RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.1 Relations & Their Properties 8.1.7

SYMMETRY PROPERTY of RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.1.8 Chapter 8 Relations

CLASSROOM EXERCISE

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.1 Relations & Their Properties 8.1.9

ANTISYMMETRY PROPERTY OF RELATIONS

CLASSROOM EXERCISE

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.1.10 Chapter 8 Relations

TRANSITIVITY PROPERTY OF RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.1 Relations & Their Properties 8.1.11

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.3 Representing Relations 8.3.1

8.3 REPRESENTING RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.3.2 Chapter 8 Relations

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.3 Representing Relations 8.3.3

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.3.4 Chapter 8 Relations

DIGRAPHS and RELATIONAL PROPERTIES

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.3 Representing Relations 8.3.5

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.3.6 Chapter 8 Relations

COMPUTING WITH A DIGRAPH

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.4 Closures of Relations 8.4.1

8.4 CLOSURES OF RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.4.2 Chapter 8 Relations

CLASSROOM EXERCISE

CLASSROOM EXERCISES

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.5 Equivalence Relations 8.5.1

8.5 EQUIVALENCE RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.5.2 Chapter 8 Relations

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.5 Equivalence Relations 8.5.3

FINITE EQUIVALENCE RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.5.4 Chapter 8 Relations

INFINITE EQUIVALENCE RELATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.6 Partial Orderings 8.6.1

8.6 PARTIAL ORDERINGS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.6.2 Chapter 8 Relations

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.6 Partial Orderings 8.6.3

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.6.4 Chapter 8 Relations

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.6 Partial Orderings 8.6.5

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.6.6 Chapter 8 Relations

INCOMPARABILITY

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.6 Partial Orderings 8.6.7

TOTAL ORDERINGS and LINEAR EXTENSIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.6.8 Chapter 8 Relations

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.6 Partial Orderings 8.6.9

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.6.10 Chapter 8 Relations

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.6 Partial Orderings 8.6.11

LUB’s GLB’s and LATTICES

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.6.12 Chapter 8 Relations

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 8.6 Partial Orderings 8.6.13

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

8.6.14 Chapter 8 Relations

coursenotes by Prof. J. L. Gross for Rosen 6th Edition