• Interaction With Powersets and Rings. The quintuple $\webleft (\mathcal{P}\webleft (X\webright ),\mathbin {\triangle },\cap ,\emptyset ,X\webright )$ is a commutative ring.[1]

Footnotes

[1] Dangerous Bend SymbolWarning: The analogous statement replacing intersections by unions (i.e. that the quintuple $\webleft (\mathcal{P}\webleft (X\webright ),\mathbin {\triangle },\cup ,\emptyset ,X\webright )$ is a ring) is false, however. See [Proof Wiki, Symmetric Difference With Union Does Not Form Ring] for a proof.


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