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5.1.  Domains and Ranges

Definition 5.3 (Domain)

Let R be a relation from X to Y. The domain of R, abbreviated by the dom R, is the set of all elements x [isin] X that occurs in at least one pair of (x, y) [isin] R. This can be expressed by

dom R = { x | x [isin] X and it exists an y [isin] Y with (x, y) [isin] R }


Definition 5.4 (Range)

Let R be a relation from X to Y. The range of R, abbreviated by the ran R, is the set of all elements y [isin] Y that occur in at least one pair of (x, y) [isin] R. This can be expressed by

ran R = { y | y [isin] Y and it exists an x [isin] X with (x, y) [isin] R }


Examples:

A graphically representation of the relation [larr] board

Definition 5.5 (Relation on A)

Let A be a set, and let R be a relation from A to A. Then R is said to be a relation on A.

Examples:


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

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