Chapter 2 laid down the basics of set theory. This fourth chapter will build on those basics and introduce some more set-theory concepts that will be used in Part 2 of this book as tools to define a database design formally—including all constraint specifications.

In the section “Binary Relations,” we’ll revisit ordered pairs and the Cartesian product to introduce the concept of a binary relation between two sets. As you’ll see, such a binary relation is in fact a subset of the Cartesian product of two sets.

The section “Functions” then introduces the important concept of a function. A function is a special kind of binary relation—one that conforms ...

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