I think there isn't so much math as just the way different people notate their logic. Personally, I use + to mean AND ("Josie+Monday" means a circle found for Josie on Monday). Though I generally write out ORs on this forum, if I make notes for myself I use | ("Josie+Monday+(Green|Purple)" means that same circle found, plus all that combined with either Green or Purple).
If I was true to my C/C++ programming roots when doing logic puzzles, I'd use &&
rather than +
(and || rather than just |), but computer programmers in general probably understand my notation without thinking too hard. The +
is easier to read in my typical scribbling than &