Symmetric Relation

A Relation R ⊆ A × A 𝑅 𝐴 𝐴 R\subseteq A\times A is symmetric if for all x , y : A : 𝑥 𝑦 𝐴 x,y:A , R ⁢ ( x , y ) ⇒ R ⁢ ( y , x ) ⇒ 𝑅 𝑥 𝑦 𝑅 𝑦 𝑥 R(x,y)\Rightarrow R(y,x) . Equivalently, a relation R 𝑅 R is symmetric if it is equal to its own Converse; this version works better in an Allegory.