N-Ary Relations

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Is any set of \( n \)-tuples, that can be used to express a [see page 6, relation] between variables. Membership in this set specifies that there exists a relation between the tuple entries. For example if we define a relation between the set of people \( P \) and locations \( L \) we'll get a binary relation (set of tuples of size 2) which is a subset of \( P \times L \).

Any predicate over \( n \) variables defines a subset of a cartesian product.

For example a tuple of size 2 between the set of persons and the set of locations can express the binary relation "lives in". If the relation contains the tuple (Alice, Crookes) it means "Alice lives in Crookes".

Graphs can help [see page 25, visualise] relations.