Inclusion (Boolean algebra) (original) (raw)
In Boolean algebra, the inclusion relation is defined as and is the Boolean analogue to the subset relation in set theory. Inclusion is a partial order. The inclusion relation can be expressed in many ways: * * * * * * The inclusion relation has a natural interpretation in various Boolean algebras: in the subset algebra, the subset relation; in arithmetic Boolean algebra, divisibility; in the algebra of propositions, material implication; in the two-element algebra, the set { (0,0), (0,1), (1,1) }. Some useful properties of the inclusion relation are: * *
| Property | Value |
|---|---|
| dbo:abstract | In Boolean algebra, the inclusion relation is defined as and is the Boolean analogue to the subset relation in set theory. Inclusion is a partial order. The inclusion relation can be expressed in many ways: * * * * * * The inclusion relation has a natural interpretation in various Boolean algebras: in the subset algebra, the subset relation; in arithmetic Boolean algebra, divisibility; in the algebra of propositions, material implication; in the two-element algebra, the set { (0,0), (0,1), (1,1) }. Some useful properties of the inclusion relation are: * * The inclusion relation may be used to define Boolean intervals such that . A Boolean algebra whose carrier set is restricted to the elements in an interval is itself a Boolean algebra. (en) |
| dbo:wikiPageExternalLink | https://books.google.com/books%3Fid=UhVebrxXGQMC&pg=PA34 |
| dbo:wikiPageID | 40153832 (xsd:integer) |
| dbo:wikiPageLength | 1433 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1096649295 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Propositional_formula dbr:Material_conditional dbr:Divisor dbc:Boolean_algebra dbr:Boolean_algebra_(structure) dbr:Set_theory dbr:Partial_order dbr:Subset |
| dbp:wikiPageUsesTemplate | dbt:Ill dbt:Isbn |
| dct:subject | dbc:Boolean_algebra |
| rdfs:comment | In Boolean algebra, the inclusion relation is defined as and is the Boolean analogue to the subset relation in set theory. Inclusion is a partial order. The inclusion relation can be expressed in many ways: * * * * * * The inclusion relation has a natural interpretation in various Boolean algebras: in the subset algebra, the subset relation; in arithmetic Boolean algebra, divisibility; in the algebra of propositions, material implication; in the two-element algebra, the set { (0,0), (0,1), (1,1) }. Some useful properties of the inclusion relation are: * * (en) |
| rdfs:label | Inclusion (Boolean algebra) (en) |
| owl:sameAs | freebase:Inclusion (Boolean algebra) wikidata:Inclusion (Boolean algebra) https://global.dbpedia.org/id/fYZd |
| prov:wasDerivedFrom | wikipedia-en:Inclusion_(Boolean_algebra)?oldid=1096649295&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Inclusion_(Boolean_algebra) |
| is dbo:wikiPageDisambiguates of | dbr:Inclusion |
| is dbo:wikiPageRedirects of | dbr:Boolean_inclusion |
| is dbo:wikiPageWikiLink of | dbr:Inclusion dbr:Subset dbr:Boolean_inclusion |
| is foaf:primaryTopic of | wikipedia-en:Inclusion_(Boolean_algebra) |