Relations: Difference between revisions
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A n-ary relation on sets A<sub>1</sub>, A<sub>2</sub>, .... A<sub>n</sub> is a subset of the Cartesian product A<sub>1</sub> x A<sub>2</sub> x ... x A<sub>n</sub>. | A n-ary relation on sets A<sub>1</sub>, A<sub>2</sub>, .... A<sub>n</sub> is a subset of the Cartesian product A<sub>1</sub> x A<sub>2</sub> x ... x A<sub>n</sub>. | ||
An example of a binary relation on a finite set is the [[Graph#Concepts|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. | |||
=TODO= | =TODO= | ||
<font color=darkgray>[[CLRS]] page 1163</font> | <font color=darkgray>[[CLRS]] page 1163</font> | ||
Revision as of 21:46, 27 August 2018
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.
TODO
CLRS page 1163