Symmetric relations

Kind of the binary relation in the symmetry-related (たいしょうかんけい British: Symmetric relation) mathematics. When binary relation R in meeting X is "symmetry", about all a belonging to X and b, I say that bRa is managed if aRb is managed.

I am as follows when I describe it mathematically.

${\displaystyle \forall a,b\in X,\ aRb\Rightarrow \;bRa}$

Symmetric relations and the antisymmetric relations (if aRb and bRa b = a) are not opposite meanings exactly. There are the symmetric and antisymmetry-like relations, too (equal signs), and is symmetric, and there are the antisymmetry-like relations, too (divisor), and is symmetric, but antisymmetry-like relations (joint relations in the congruence equation) is not symmetric, but there are the antisymmetry-like relations (<= and >=), too.

Attribute including symmetric relations

Equivalence relation - transitional and reflex symmetric relations

Example

• "I am married" (in A with B) is a symmetric relation, but "it is small" (in A from B) is not a symmetric relation.
• "It is equal (in A with B) (equation).
• "A is an odd number and B is an odd number, too"

Allied item

• Asymmetry relations

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This article is taken from the Japanese Wikipedia Symmetric relations

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