Discrete Mathematics and Combinatorics

Chapter 2

Sets, Functions and Relations

Learning Objectives

On completing this chapter, you should able to:

• work with the concepts of a set, its elements and subsets

• define the sets of natural numbers, integers, rational numbers, real numbers, complex numbers and their various subsets

• find unions and intersections of given sets

• define the concepts of a relation and a function

• solve problems on reflexive, symmetric and transitive relations

• solve problems on one-to-one and onto functions

• find the images of subsets of domains and inverse images of subsets of the co-domain for some simple functions

• find left inverses, right inverses and the inverse of some simple functions whenever they exist

• prove basic results on one-one and onto functions ...