How to express a "some of which are" and "not all are" relationship with enhanced entity-relationship diagrams? For example:

Gardens have attribute gate, Condos have attribute door. Some of the Gardens and Condos are Private_Properties. On the other hand, Private_Properties are not restricted to only Gardens or Condos.

How can these non-exclusive relationship be illustrated with an enhanced entity-relationship diagram (EERD)?
You can represent a 1..* relationship

Notation is quite standard but it may vary a little depending on your EER tool... Since I work with Oracle, I'm used to Oracle Data Modeler notation... 

Check the picture... and good luck!