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* The set of all subsets of ''S'' that are either finite or [[cofinite]] is a Boolean algebra.
* For any [[natural number]] ''n'', the set of all positive [[divisor]]s of ''n'' forms a [[distributive lattice]] if we write ''a'' ≤ ''b'' for ''a'' | ''b''. This lattice is a Boolean algebra if and only if ''n'' is [[square-free integer|square-free]]. The smallest element 0 of this Boolean algebra is the natural number 1; the largest element 1 of this Boolean algebra is the natural number ''n''.
* Other examples of Boolean algebras arise from [[topology|topological spaces]]: if ''X'' is a topological space, then the collection of all subsets of ''X'' which are both open and closed forms a Boolean algebra with the operations ∨ := ∪ (union) and ∧ := ∩ (intersection).
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