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 X that occurs in at
least one pair of (x, y) R. This can be expressed by
dom R = { x  x X and it exists an y Y with (x, y) 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 Y that occur in at
least one pair of (x, y) R. This can be expressed by
ran R = { y  y Y and it exists an x X with (x, y) R }
Examples:


A = { 1, 2, 3, 4 } and
B = { a, b, c, d } and the relation is given by
R = { (2,c), (1,d), (1,a), (3, c) }.
ran R = { 1, 2, 3} and
dom R = { a, c ,d }
A graphically representation of the relation 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:


R = { (x,y) Nat × Nat and y = x! }
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© by HansPeter Bischof. All Rights Reserved (1998).
Last modified: 27/July/98 (12:14)