This section considers (in the form of theorems and conjectures) whether properties (reflexivity, symmetry, transitivity) of funcoids and reloids are preserved an reflected by their relationships (functions $(\mathsf{FCD})$, $(\mathsf{RLD})_{\mathrm{in}}$, $(\mathsf{RLD})_{\mathrm{out}}$ which map between funcoids and reloids).