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Domain and Codomain of a Relation


If R is a relation from the set A to the set B, then the domain of R is the set of all first components of the ordered pairs in the relation R.
 
The whole set B is called the codomain of the relation.

For instance, let A = {1, 2, 4, 5} and B = {1, 4, 8, 16, 25, 64, 125, 216}. Define R from A to B by x R y if x3 = y. Then the domain of R is the set {1, 2, 4, 5} and the codomain is {1, 4, 8, 16, 25, 64, 125, 216}

Consider the sets

Consider the relation defined from A to B

For this relation the domain is

And the codomain is





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