A Relation R : A → A → Ω : 𝑅 → 𝐴 𝐴 → Ω R:A\to A\to\Omega is connected if for all x , y : A : 𝑥 𝑦 𝐴 x,y:A , ¬R(x,y)∧¬R(y,x)⇒x=y⇒𝑅𝑥𝑦𝑅𝑦𝑥𝑥𝑦\lnot R(x,y)\land\lnot R(y,x)\Rightarrow x=y . In other words, the Converse of R 𝑅 R is an Antisymmetric Relation.
¬R(x,y)∧¬R(y,x)⇒x=y⇒𝑅𝑥𝑦𝑅𝑦𝑥𝑥𝑦\lnot R(x,y)\land\lnot R(y,x)\Rightarrow x=y