Relations
Jump to navigation
Jump to search
Internal
Overview
A binary relation R on two sets A and B is a subset of the Cartesian product A x B. If (a, b) belongs to the subset of the Cartesian product that defines the relation, we write a R b.
A binary relation R on a set A is a subset of the Cartesian product A x A.
A n-ary relation on sets A1, A2, .... An is a subset of the Cartesian product A1 x A2 x ... x An.
An example of a binary relation on a finite set is the edge set of a graph.
Binary Relation Properties
A binary relation R ⊆ A x A is reflexive if a R a for all a ∈ A.
A binary relation R ⊆ A x A is symmetric if a R b implies b R a for all a, b ∈ A.
TODO
CLRS page 1163