Definition:Relational Structure

Definition
A relational structure $\left ({S, \mathcal R}\right)$ is a set $S$ together with a relation $\mathcal R$ on $S$.

Technically, $\left ({S, \mathcal R}\right)$ is an ordered pair:
 * The first element of the pair is the set $S$.
 * The second element is the relation $\mathcal R$, which is itself a set of ordered pairs (being a subset of the cartesian space $S^2$).