symmetry

of a relation

Also known as: symmetrical relation

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July 14, 2026

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In logic and mathematics, a relation is a set of ordered pairs, triples, or longer tuples. A relation is considered symmetric if, whenever it holds between two objects, say x and y, it also holds between y and x. A common example of a symmetric relation is "is parallel to". For instance, if line A is parallel to line B, then line B is also parallel to line A. Other properties of relations include transitivity and reflexivity.12

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formal logic
Classification of dyadic relations
…is true is called a symmetrical relation (example: “is parallel to”). If the relation ϕ is such that, whenever it holds between one object and a second, it fails to hold between the second and the first—i.e., if ϕ is such that (∀x)(∀y)(ϕxy ⊃ ∼ϕyx) —then ϕ is said to…
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…is true is called a symmetrical relation (example: “is parallel to”). If the relation ϕ is such that, whenever it holds between one object and a second, it fails to hold between the second and the first—i.e., if ϕ is such that (∀x)(∀y)(ϕxy ⊃ ∼ϕyx) —then ϕ is said to…
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set theory
Relations in set theory
…property are said to be symmetric. (Note that the ordering relation is not symmetric.) These examples also have the property that whenever one object bears the relation to a second, which further bears the relation to a third, then the first bears that relation to the third—e.g., if a <…
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…property are said to be symmetric. (Note that the ordering relation is not symmetric.) These examples also have the property that whenever one object bears the relation to a second, which further bears the relation to a third, then the first bears that relation to the third—e.g., if a <…
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