relation properties.tex (564B)
1 \begin{tabular}{@{}l l@{}} 2 \toprule 3 Property & Condition \\ 4 \midrule 5 Injective & \(r\relationComposition\breve{r} \relationOr \relationIdentity = \relationIdentity\) \\ 6 Functional & \(\breve{r} \relationComposition r \relationOr \relationIdentity = \relationIdentity\) \\ 7 Symmetric & \(r = \breve{r}\) \\ 8 Transitive & \(r\relationComposition r \relationOr r = r\) \\ 9 Left-restriction & \(r\relationComposition \breve{r} \relationOr 1_X = 1_X\) \\ 10 Right-restriction & \(\breve{r}\relationComposition r \relationOr 1_X = 1_X\) \\ 11 \bottomrule 12 \end{tabular}