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...

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

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...

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...

Boolean ring, with symmetric difference as the addition of the ring and intersection as the multiplication of the ring. The symmetric difference is equivalent...