IF \(C\) and \(D\) are non-empty disjoint \(C \cap D = \emptyset\), and \(C\) and \(D\) are convex sets, \(\exists a \neq 0\) such that:

\begin{equation} a^{T} x \leq b, x \in C \end{equation}

\begin{equation} a^{T}x \geq b, x \in D \end{equation}

The hyperplane:

\begin{equation} \qty {x \mid a^{T} x = b} \end{equation}

separates \(C, D\) such that \(a^{T}x \geq b, a^{T}x \leq b\).