I'm not good at making drawings, but I hope that this will be appreciated for its content if not for its design
Open Source, Proprietary, P.D. (Public Domain), are sharp-edge definitions, so are the various "free software" licenses, which are also mostly either/or: if it's GPL then it's not MIT, LGPL, Apache, etc and if it's MIT it's not GPL, LGPL, Apache, etc. (some are strictly included, as for example Affero being a strict subset of GPL.)
On the other hand, the very definition of Free software is blurry and depends on whom you're talking to. It definitely includes licenses like MIT and GPL, it definitely implies being Open Source, it definitely is incompatible with being Proprietary, I'm not so sure how it relates to Public Domain, my personal perception is that they are disjoint, but that depends on where I place the blurry line.
Public Domain software is a strange beast. As said, it's my interpretation to put it outside of the Free Software. Whether you get the sources, or not, depends on what the author of the software decided to do. So, if it's Public Domain and you get the sources, it is not Proprietary. If it's Public Domain and you do not get the sources, you can call it Proprietary.
Please note that I'm nowhere speaking of price, that's a totally different story, independent from what we're discussing here.
I just found a more complete version of my diagram, a bit of an overkill given the OP question. It includes → the "free/gratis" category, → it uses the term "copylefted" for what I here call "free/libre", → it includes a new category for "freely downloadable", → it shows the position of "shareware", → and corrects my initial misconception that P.D. is necessarily Open Source:
so, short answer: Public Domain may be Open Source, or not.