An D21: Algebraic structure $G = (X, +)$ is a semigroup if and only if

(1)	\begin{equation} \forall \, x, y \in X : x + y \in X \end{equation}
(2)	\begin{equation} \forall \, x, y, z \in X : (x + y) + z = x + (y + z) \end{equation}