# Connected Relation **A [[relation]] that relates all distinct elements to each other.** > [!NOTE] Connected Relation > A *connected* or a *complete* or *total relation* is a binary relation $R$ on a [[set]] $X$ such that for every $x, y\in X$, if $x\neq y$, then $xRy$ or $yRx$. > $\forall\;x,y\in X: x\neq y\implies (xRy\vee yRx))$ > > Equivalently, for every $x, y\in X$, $xRy$ or $yRx$ or $x=y$. > [!NOTE] Strongly Connected Relation > A *strongly connected relation* is a binary relation $R$ on a set $X$ such that for every $x, y\in X$, $xRy$ or $yRx$. > > That is, it relates *every pair* of elements to each other.