Category:Algebras of Sets
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This category contains results about Algebras of Sets.
Definitions specific to this category can be found in Definitions/Algebras of Sets.
Let $X$ be a set.
Let $\powerset X$ be the power set of $X$.
Let $\RR \subseteq \powerset X$ be a set of subsets of $X$.
Then $\RR$ is an algebra of sets over $X$ if and only if the following conditions hold:
\((\text {AS} 1)\) | $:$ | Unit: | \(\ds X \in \RR \) | |||||
\((\text {AS} 2)\) | $:$ | Closure under Union: | \(\ds \forall A, B \in \RR:\) | \(\ds A \cup B \in \RR \) | ||||
\((\text {AS} 3)\) | $:$ | Closure under Complement Relative to $X$: | \(\ds \forall A \in \RR:\) | \(\ds \relcomp X A \in \RR \) |
Pages in category "Algebras of Sets"
The following 5 pages are in this category, out of 5 total.