symmetric relation
An example of a symmetric relation on {a,b,c} is {(a,a),(c,b),(b,c),(a,c),(c,a)}. One relation that is not symmetric is ℛ={(b,b),(a,b),(b,a),(c,b)}, because (c,b)∈ℛ but (b,c)∉ℛ.
On a finite set with n elements there are 2n2 relations, of which 2n2+n2 are symmetric.
A relation ℛ that is both symmetric and antisymmetric has the property that xℛy implies x=y. On a finite set with n elements there are only 2n such relations.
Title | symmetric relation |
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Canonical name | SymmetricRelation |
Date of creation | 2013-03-22 12:15:39 |
Last modified on | 2013-03-22 12:15:39 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 21 |
Author | yark (2760) |
Entry type | Definition |
Classification | msc 03E20 |
Related topic | Reflexive |
Related topic | Transitive3 |
Related topic | Antisymmetric |
Defines | symmetry |
Defines | symmetric |