I have added a new section “Properties preserved by relationships” to my math research book.

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 $latex (\mathsf{FCD})$, $latex (\mathsf{RLD})_{\mathrm{in}}$, $latex (\mathsf{RLD})_{\mathrm{out}}$ which map between funcoids and reloids).