Given that "A" is one set and "B" and "C" are another set, how should the following phrase be punctuated correctly?
A and B and C
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You can write the matched pair with an ampersand instead of the word and to indicate that they are closer than the other items in the list:
We ordered spaghetti and fish & chips.
This usage isn't universal, although Wikipedia notes some specific cases where it's preferred:
In film credits for stories, screenplays, etc., & indicates a closer collaboration than and. The ampersand is used by the Writers Guild of America to denote two writers collaborating on a specific script, rather than one writer rewriting another's work. . . .
The ampersand can be used to indicate that the "and" in a listed item is a part of the item's name and not a separator (e.g. "Rock, pop, rhythm & blues, and hip hop").
If you're working with a particular style guide, it may have advice on whether ampersands are preferred (or forbidden) for these kinds of cases.