A relation from set A to set B is a subset of their Cartesian product, AxB. A relation between two sets is also called a binary relation. Relations between more than two sets are called n-ary relations.

More formally, a binary relation is defined as an ordered triple: (A, B, R). A is the domain of the relation, B is the codomain, and R is the subset of A x B, also known as the relation’s graph.

Since R by definition is a set of ordered pairs (a, b), then for all ordered pairs (a, b) where a \in A and b \in B, one, and only one of the following must be true:

  • (a, b) \in R; this is read “a is R-related to b” and is written aRb.
  • (a, b) \notin R; this is read “a is not R-related to b” and is written a\cancel{R}b.

Some properties of binary relations:

  • reflexive
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