INTRODUCTION TO RELATIONS AND FUNCTIONS

Introduces Relations and Functions through exploration of key definitions, concepts, theorems and worked examples.

1.1 Introduction 3
1.2 Ordered Pair 3
1.3 Cartesian Product of Two sets 3
1.4 Relation 10
1.5 Inverse of a Relation 11
1.6 Classification of Relation 12
1.7 Equivalence Relations 13
1.8 Composition of Relations 14
1.9 Relations other than Equivalence 20
2.10 Functions 23
2.11 Types of Functions 24
2.12 Some Particular Functions 32
1.13 Algebra of Functions 36
1.14 Composition of Functions 37
1.15 Binary Operations 47
1.16 Properties of Binary Operation 48
1.17 Composition Table for Binary Compositions on Finite Sets 50
1.18 Recursively Defined Functions 59
1.19 Partial and Total Functions 60
1.20 Primitive Recursive Function 60
1.21 Some Recursive Functions 61
1.22 Functions for Computer Science 62
1.23 Growth of Functions 65