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O que (quem) é symmetric relation - definição

TYPE OF BINARY RELATION

Antisymmetric relation

BINARY RELATION SUCH THAT IF A IS RELATED TO B AND IS DIFFERENT FROM IT THEN B IS NOT RELATED TO A

Anti-symmetric relation

In mathematics, a binary relation $R$ on a set $X$ is antisymmetric if there is no pair of distinct elements of $X$ each of which is related by $R$ to the other. More formally, $R$ is antisymmetric precisely if for all $a,b\in X,$

or equivalently, The definition of antisymmetry says nothing about whether

aRa

actually holds or not for any

a

. An antisymmetric relation

R

on a set

X

may be reflexive (that is,

aRa

for all

a\in X

), irreflexive (that is,

aRa

for no

a\in X

), or neither reflexive nor irreflexive. A relation is asymmetric if and only if it is both antisymmetric and irreflexive.

https://en.wikipedia.org/wiki/Antisymmetric_relation

Finitary relation

PROPERTY THAT ASSIGNS TRUTH VALUES TO K-TUPLES OF INDIVIDUALS

Unary relation; N-ary relation; Nary relation; Kary relation; Dyadic Relation; Polyadic relation; Theory of relations; N-ary relations; Relation (logic); Quaternary relation; Subrelation

In mathematics, a finitary relation over sets is a subset of the Cartesian product ; that is, it is a set of n-tuples consisting of elements xi in Xi. Typically, the relation describes a possible connection between the elements of an n-tuple.

https://en.wikipedia.org/wiki/Finitary_relation

False relation

TYPE OF DISSONANCE IN POLYPHONIC MUSIC

Cross-relation; Cross relation; Non-harmonic relation

A false relation (also known as cross-relation, non-harmonic relation) is the name of a type of dissonance that sometimes occurs in polyphonic music, most commonly in vocal music of the Renaissance.

https://en.wikipedia.org/wiki/False_relation

Wikipédia

Symmetric relation

A symmetric relation is a type of binary relation. An example is the relation "is equal to", because if a = b is true then b = a is also true. Formally, a binary relation R over a set X is symmetric if:

\forall a,b\in X(aRb\Leftrightarrow bRa),

where the notation $aRb$ means that $(a,b)\in R$ .

If R^T represents the converse of R, then R is symmetric if and only if R = R^T.

Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation.

https://en.wikipedia.org/wiki/Symmetric relation