Which kind of operations on a power set leads to a group/monoid?
Known to me are: - intersection - union - symmetric difference - complex product of a group
Ate there some more examples?
2026-03-25 14:19:19.1774448359
Operations on power set
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The power set of any set becomes an Abelian group under the operation of symmetric difference, with the empty set as the neutral element of the group and every element in this group being its own inverse. The power set of any set becomes a Boolean ring with symmetric difference as the addition of the ring and intersection as the multiplication of the ring. Here is the proof, that symmetric difference on power set forms Abelian group. The proof of the statement that the power set of any set with intersection is commutative monoid here.
Just for the curiosity the Ring of sets wikipedia article is also related.