Sections, concepts, and problems

6.1. Relations and their properties. (Binary) relations. What makes a relation reflexive, symmetric, antisymmetric, and transitive. Composition and powers of relations.
3abf, 5dg ((g) is antisymmetric!), 13, 17, 19, 27, 29

6.3. Representing relations. Representing relations by directed graphs and zero-one matrices. How to recognize certain types of relations (reflexive, symmetric, etc.) by their graphs or matrices. How to compute the matrix for a union, intersection, or composition of two relations.
1c, 5, 7c, 8abc, 10c, 15, 17

6.5. Equivalence relations. Equivalence relations, equivalence classes, and partitions.
1d, 3a, 5, 7, 11, 13, 29 [look at the directed graph], 35 [think partitions]

6.6. Partial orderings. Partially ordered sets ("posets"), comparable elements, totally ordered sets, well-ordered sets, Hasse diagrams, lexicographic orderings on strings and Cartesian products.
1, 3, 5, 9, 13, 15, 17

Other Chapters

Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 6