\begin{definition}[Definition:Agreement/Relations]
Let:
:$(1): \quad \RR_1 \subseteq S_1 \times T_1$ be a relation on $S_1 \times T_1$
:$(2): \quad \RR_2 \subseteq S_2 \times T_2$ be a relation on $S_2 \times T_2$
:$(3): \quad X \subseteq S_1 \cap S_2$
Let:
:$\forall s \in X: \map {\RR_1} s = \map {\RR_2} s$
where $\map {\RR_1} s$ denotes the image of $s$ under $\RR$:
:$\map {\RR_1} s := \set {t \in T: s \mathrel {\RR_1} t}$
Then the relations $\RR_1$ and $\RR_2$ are said to '''agree on''' or '''be in agreement on''' $X$.
Category:Definitions/Relation Theory
\end{definition}