Sections, concepts, and problems

Section 1. Relations. Relations from one set to another, domain, range, diagonal relations on a set, reflexive relations, symmetric relations, transitive relations, antisymmetric relations, Cartesian and directed graphs of relations (the latter done in class)
2, 4b, 5d, 6c, 7c, 11a

Section 2. Equivalence Relations. Equivalence relations, equivalence classes, partitions, congruence modulo n
1a, 2b, 3b, 3d, 4abc, 8c

Section 3. Partial Orders. Posets, total/linear ordered sets and some of their properties, maximum element, maximal elements, mimimum element, minimal elements, upper bounds, least upper bound (supremum), lower bounds, greatest lower bound (infimum), complete posets, subposets
2, 4bf, 7a, 7b, 8a, 14a

Section 4. Quotient Spaces. Quotient spaces and three applications: identification spaces in topology (not in book), quasiorders and quotient spaces, and algebraic structures and quotient spaces.
2, 6, 7bd, 11a

Other Chapters

Chap 1 | Chap 2 | Chap 3 | Chap 4 | Chap 5 | Chap 6