A symmetric relation is a type of binary relation. Formally, a binary relation R over a set X is symmetric if: ∀ a , b ∈ X ( a R b ⇔ b R a ) , {\displaystyle...

mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in...

other's bills, the relation is antisymmetric. Partial and total orders are antisymmetric by definition. A relation can be both symmetric and antisymmetric...

of) quasi-reflexivity. Symmetric for all x, y ∈ X, if xRy then yRx. For example, "is a blood relative of" is a symmetric relation, because x is a blood...

asymmetric, anti-symmetric, left-unique, or right-unique, then so is R. A relation is reflexive, irreflexive, symmetric, asymmetric, anti-symmetric, connected...

a symmetric polynomial if for any permutation σ of the subscripts 1, 2, ..., n one has P(Xσ(1), Xσ(2), ..., Xσ(n)) = P(X1, X2, ..., Xn). Symmetric polynomials...

simultaneously reflexive, symmetric, and transitive – in other words, equivalence relations – (sequence A000110 in the OEIS), those that are symmetric and transitive...

relation that is symmetric and transitive. If the relation is also reflexive, then the relation is an equivalence relation. Formally, a relation R {\displaystyle...

{\displaystyle x=y.} A relation R {\displaystyle R} is coreflexive if and only if its symmetric closure is anti-symmetric. A reflexive relation on a nonempty set...

{\displaystyle \geq } . A binary relation is equal to its converse if and only if it is symmetric. If R {\displaystyle R} is a binary relation over sets X {\displaystyle...