Will give describe the relationship between: the domain, relation, and range

Relations are subsets of products A×BA×B where AA is the domain and BB the codomain of the relation.

A function ff is a relation with a special property: for each a∈Aa∈A there is a unique b∈Bb∈B s.t. ⟨a,b⟩∈f⟨a,b⟩∈f.

This unique bb is denoted as f(a)f(a) and the 'range' of function ff is the set {f(a)∣a∈A}⊆B{f(a)∣a∈A}⊆B.

You could also use the notation {b∈B∣∃a∈A[⟨a,b⟩∈f]}{b∈B∣∃a∈A[⟨a,b⟩∈f]}

Applying that on a relation RR it becomes {b∈B∣∃a∈A[⟨a,b⟩∈R]}{b∈B∣∃a∈A[⟨a,b⟩∈R]}

That set can be labeled as the range of relation RR.

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