'quantum mechanics is not a superset of quantum electrodynamics' 

Um. It so is dude.

QED is the theory of quantum mechanics as it applies to light, (in other words, photons, electrons and protons); but it doesn't cover quarks (see QCD for that).

The idea that it isn't part of quantum mechanics and thus quantum mechanics isn't a superset is unbelievable. Do you have a cite for that?