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## Inside this book

The concept of a set underlies most of the modem mathematics and much of computer science. To use sets as a foundation for all the other structures in this text, we first need to understand both the language used to describe sets and the operations normally associated with sets. The language of sets is very precise. When we use this language carefully, we gain precision in expressing problems and describing solutions to problems. Understanding basic operations on sets and the properties of these operations is a model for the approach that is used to introduce most other discrete structures in this text.

In extending our understanding of operations on sets, we will learn proof techniques to explore other discrete mathematical topics, such as relations, functions, and graphs. We will use these proof techniques, for example, to prove that algorithms are correct and to determine how well we have chosen an algorithm for a given task.

This chapter has five main sections. The first introduces the notion of a set and the language for describing collections of elements. In addition, this section introduces several proof templates that are guided to both understanding and constructing proofs. The second deals with the common operations on sets: unions, intersections, complements, products, and the power set of a set. Some additional proof templates are introduced that are drawn from proofs in this section.