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N-ary relations

Let A ₁, A ₂, …, A_n be sets. An n-ary relation on these sets is a subset of . The sets A ₁, A ₂, …, A_n are called the domains of the relation, and n is called its degree.

Example. Let R be the relation consisting of triples (a, b, c), where a, b and c are integers with a < b < c. Then , but . The degree of this relation is 3. Its domains are all equal to the set of integers.

Example. Let R be the relation consisting of 5-tuples (A, N, S, D, T) representing airplane flights, where A is the airline, N is the flight number, S is the starting point, D is the destination, and T is the departure time. For instance, if Nadir Express Airplanes has flight 963 from Newark to Bangor at 15:00, then (Nadir, 963, Newark, Bangor, 15:00) belongs to R. The degree of this relation is 5, and its domains are the set of all airlines, the set of flight numbers, the set of cities, the set of cities (again), and the set of times.