Editing Algebra of sets (section)

{{short description|Identities and relationships involving sets}}
{{about|algebraic properties of set operations in general|a boolean algebra of sets|Field of sets}}
{{more footnotes needed|date=April 2023}}
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Before changing the first sentence: 
The terminology "an algebra of sets" is much more well known than "the algebra of sets" (as described on this article's talk page). As a rule, a reader should be able to figure out just by reading the first sentence of the lead whether or not they are at the right article. So readers should be clearly informed that this article is not about "an algebra of sets".
See [[MOS:LEADSENTENCE]] and [[Wikipedia:Summary style]]
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In [[mathematics]], '''the algebra of sets''', not to be confused with the [[mathematical structure]] of [[Field of sets|''an'' algebra of sets]], defines the properties and laws of [[Set (mathematics)|sets]], the set-theoretic [[operation (mathematics)|operations]] of [[union (set theory)|union]], [[intersection (set theory)|intersection]], and [[complement (set theory)|complementation]] and the [[binary relation|relations]] of set [[equality (mathematics)|equality]] and set [[subset|inclusion]]. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.

Any set of sets closed under the set-theoretic operations forms a [[Boolean algebra (structure)|Boolean algebra]] with the join operator being ''union'', the meet operator being ''intersection'', the complement operator being ''set complement'', the bottom being {{tmath|1= \varnothing }} and the top being the [[universe (mathematics)|universe]] set under consideration.