Course 2BA1, 2008–09 Section 2: Sets and Functions

2 Sets and Functions 10 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 10 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 14 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.7 Partitions and Equivalence Relations . . . . . . . . . . . . . . 18 2.8 Partial Orders and Lattices . . . . . . . . . . . . . . . . . . . 19 2.9 Cartesian Products of Sets . . . . . . . . . . . . . . . . . . . . 20 2.10 Functions between Sets . . . . . . . . . . . . . . . . . . . . . . 22 2.11 Compositions of Functions . . . . . . . . . . . . . . . . . . . . 23 2.12 The Graph of a Function . . . . . . . . . . . . . . . . . . . . . 23 2.13 The Inverse of a Function . . . . . . . . . . . . . . . . . . . . 24 2.14 Injective, Surjective and Bijective Functions . . . . . . . . . . 25 2.15 Functions defined on Finite Sets . . . . . . . . . . . . . . . . . 28