# Explain the difference between the domain and the range of a relation.

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### 1 Answer

A relation is a set of ordered pairs (a,b) where a comes from some set A and b comes from a set B. A is called the domain and B is the range.

(The domain is typically thought of as the set of all possible inputs, while the range is the set of all possible outputs.)

Thus the relation {(1,2),(1,3),(2,3)} has a domain of {1,2} and a range of {2,3}. It is relatively easy to list the domain or range in a small finite relation. If the relation is infinite then you can use set builder notation.

E.g. the relation f(x)=2x for integer x takes an integer input x and returns an integer output y. Note that y is always an even number.

The domain would be `D={x|x in ZZ}` and the range would be `R={2k|k in ZZ}`