CHAPTER V - CARTESIAN PRODUCTS OF SETS. RELATIONS. FUNCTIONS AS RELATIONS

Abstract

This chapter describes the Cartesian products of sets, relations, and functions as relations. The set of all ordered pairs (x, y) such that x ∈ X and y ∈ Y is called the Cartesian product of the sets X and Y and is denoted by X × Y. Cartesian products of sets occur very often in mathematics. The Cartesian multiplication of sets is one of the elementary operations performed on sets. The set of all complex numbers—the set of points on a plane—is an example of a Cartesian product. In this chapter, binary relations are discussed. Binary relations are properties of ordered pairs, that is, properties of elements of a Cartesian product. Thus, binary relations are subsets of a Cartesian product. The chapter further describes propositional functions of two variables. Reflexive, irreflexive, symmetric, asymmetric, antisymmetric, and transitive relations are also discussed in the chapter.