How does a DM know, in D&D 5th edition, which source to refer to if there is a seeming conflict between two core rule books?
During the discussion under this question, I noted the following assertion made that seems right, but I'd like to see a formal derivation of the position.
MM supersedes PHB for stats as well as what Miniman states, PHB doesn't offer "Variant" which is the DMs choice. — this comment by XAQT78
The MM supersedes the PHB. — this answer by Ryan
While my own instinct is that the Monster Manual is a DM tool, and DM's rulings overcome other opinions and interpretations, thus MM > PHB, new DM's may be at a loss when running into a similar case where one core book leads them in one direction, and another core book leads them in a different direction.
An early discussion on Inspiration, where the tone in the PHB differs somewhat from the tone in the DMG, is a similar case.
If the MM supersedes the PHB, please explain the reasoning behind why. (Or the reverse).
Example: The example I am most familiar with, as I have the original printings, was the discrepancy between the MM and PHB stats for bears Appendix D: Creature Statistics(PHB 1st printing) where the bonus was +3 and +5 respectively. It has since been modified by PHB errata of 2018 to match the MM,
[New] Black Bear (p. 304). The to-hit bonus for both Bite and Claws is now +4. [New] Brown Bear (p. 304). The to-hit bonus for both Bite and Claws is now +6. (errata
but for just under 4 years the question could have been: which has precedence?
Note: this question does not intend to address things like the Homunculus, that in the MM does not have a discrete means of creation, while the expansion/supplement Xanathar's Guide to Everything adds such a spell/process for the PC's to use. The question's scope is limited to the core books: Player's Handbook, Monster Manual, Dungeon Masters Guide.
If a precedent was set in previous editions ...
... and this point of view is a carry over from 3.xe, and/or 4e, that would be useful in an answer.