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A relation is not good enough. We take a transformation, or map, call it M, between any two sets, A and B. Denoted M: A ---> B.

Set A is the domain, B is called the co-domain. The set of all elements in B that is a map of A, or with a minor abuse of notation, the set M(A) is called the range.

So, if you take a map M from human, A, to animals, B. For each person, we say M(person) = The person's pet. It's a perfectly fine map, or relation. Then, the domain is all human, the co-domain is the animals, and the range is all animals that are also pets.

Range is ALWAYS a subset of the co-domain.

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