Note: That's not actually a ring. If you use XOR as addition as it's a ring. You could say it's a semiring, but that's probably not the most useful descriptio

Note: That's not actually a ring. If you use XOR as addition as it's a ring. You could say it's a semiring, but that's probably not the most useful description of it. A more-fitting structure would be an appropriate sort of distributive lattice. Or really... a Boolean algebra! Except I also have to point out that you only included AND and OR; you left out NOT, which is also an important part of the structure.