Set operations follow rules {set theory}. Boolean-set algebras {algebra of sets} can be axiomatic set theories. From sets, one can choose {selection, set} smaller sets {subset, selection}, without regard for sequence or order {combination, set}. For valid set-theory statements, if operations union and intersection interchange, null set and universal set interchange, and set inclusions reverse, valid statements result. Set inclusion can use only intersection and union, so statements do not need to have set inclusion.
Mathematical Sciences>Set Theory
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Date Modified: 2022.0224