next next up down toc toc mail

5.  Relations

Definition 5.1 (Cartesian Product)

Let A and B be two sets. The set of all ordered pairs so that the first member of the ordered pair [isin] A and the second member of the ordered pair [isin] B is called the Cartesian Product. Accordingly:

A × B = { (x,y) | x [isin] A and y [isin] B }

[equation] are sets. The set of all n-tuples [equation] with [equation] , 1 [lt] i [lt] n, is denoted by

[equation]

We write: [equation] = { ( [equation] | [equation] , 1 [lt] i [lt] n }

Examples:

Definition 5.2 (Relation)

Let A and B be two sets. A relation from A to B is any set of pairs
(x,y), x[isin] A and y [isin] B.

If (x,y) [isin] R we say x is R-related to y.

To express that R is a relation from A to B we write R: A [double B

Shorthand: (x,y) [isin] R [equiv] xRy

Examples:


back next up down toc toc mail


Created by unroff & hp-tools. © by Hans-Peter Bischof. All Rights Reserved (1998).

Last modified: 27/July/98 (12:14)