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Domain and Range

Definition: domain and range of a binary relation R

• The domain of R is the set of first components of the tuples in R:

  domain(R) := {r₀: r in R}.

• The range of R is the set of second components of the tuples in R:

  range(R) := {r₁: r in R}.

forall x: x in domain(R) <=> exists y: <x, y> in R,
forall y: y in range(R) <=> exists x: <x, y> in R.