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Applied Discrete Structures

Chapter 1 Set Theory

empty set

Betty’s math teacher said, in a sweat:
"I will teach you some set theory yet!"
But his best efforts failed,
And at Betty he railed:
"Your insights? A true empty set!"
SheilaB, The Omnificent English Dictionary In Limerick Form
Many of the topics in this book are defined in terms of sets. It is essential to understand basic set theory and how it is use to define basic structures such as relation, functions, graphs and algebraic structures. We begin this chapter with some of the basic set language and notation that will be used throughout the text. We thne consider basic set operations. Venn diagrams will be introduced in order to give the reader a clear picture of these operations. In addition, we will review the binary representation of positive integers and introduce summation notation and its generalizations.