Subset, strict subset, and superset (video) | Khan Academy

Unfortunately, different mathematicians define these symbols in slightly different ways. Some say A⊂B to mean ... Ifyou'reseeingthismessage,itmeanswe'rehavingtroubleloadingexternalresourcesonourwebsite. Ifyou'rebehindawebfilter,pleasemakesurethatthedomains*.kastatic.organd*.kasandbox.orgareunblocked. CoursesSearchDonateLoginSignupSearchforcourses,skills,andvideosMaincontentMathStatisticsandprobabilityProbabilityBasicsetoperationsBasicsetoperationsIntersectionandunionofsetsRelativecomplementordifferencebetweensetsUniversalsetandabsolutecomplementSubset,strictsubset,andsupersetThisisthecurrentlyselecteditem.BringingthesetoperationstogetherPractice:BasicsetnotationNextlessonExperimentalprobabilityCurrenttime:0:00Totalduration:4:320energypointsMath·Statisticsandprobability·Probability·BasicsetoperationsSubset,strictsubset,and supersetGoogleClassroomFacebookTwitterEmailBasicsetoperationsIntersectionandunionofsetsRelativecomplementordifferencebetweensetsUniversalsetandabsolutecomplementSubset,strictsubset,andsupersetThisisthecurrentlyselecteditem.BringingthesetoperationstogetherPractice:BasicsetnotationNextlessonExperimentalprobabilityVideotranscriptLet'sdefine ourselvessomesets.Solet'ssaythesetAis composedofthenumbers1.3.5,7,and18.Let'ssaythat thesetB--letmedothisinadifferent color--let'ssaythatthesetBis composedof1,7,and18.Andlet'ssaythatthesetCis composedof18,7,1,and19.NowwhatIwanttostart thinkingaboutinthisvideoisthenotionofasubset.Sothefirstquestion is,isBasubsetofA?Andthereyoumightsay, well,whatdoessubsetmean?Well,you'reasubsetif everymemberofyoursetisalsoamember oftheotherset.Soweactuallycanwrite thatBisasubset--andthisisanotation rightoverhere,thisisasubset--Bisa subsetofA.Bisasubset.Soletmewritethatdown.BissubsetofA.Every elementinBisamemberofA.Nowwecangoevenfurther.WecansaythatBis astrictsubsetofA,becauseBisasubset ofA,butitdoesnotequalA,whichmeansthatthere arethingsinAthatarenotinB.Sowecould evengofurtherandwecouldsay thatBisastrictorsometimessaida propersubsetofA.Andthewayyoudothat is,youcouldalmostimaginethatthisiskindof alessthanorequalsign,andthenyoukindof crossoutthisequalpartofthelessthanorequalsign.Sothismeansa strictsubset,whichmeanseverythingthat isinBisamemberA,buteverythingthat'sin AisnotamemberofB.Soletmewritethis.ThisisB.Bisa strictorpropersubset.So,forexample,wecanwrite thatAisasubsetofA.Infact,everysetis asubsetofitself,becauseeveryoneofits membersisamemberofA.WecannotwritethatA isastrictsubsetofA.Thisrightoverhereisfalse.Solet'sgiveourselvesa littlebitmorepractice.Canwewritethat BisasubsetofC?Well,let'ssee.Ccontainsa1,itcontains a7,itcontainsan18.Soeverymemberof BisindeedamemberC.Sothisright overhereistrue.Now,canwewrite thatCisasubset?Canwewritethat CisasubsetofA?CanwewriteCisasubsetofA?Let'ssee.EveryelementofCneeds tobeinA.SoAhasan18,ithasa7,ithasa1.Butitdoesnothavea19.Soonceagain,this rightoverhereisfalse.Nowwecouldhave alsoadded--wecouldwriteBisasubset ofC.OrwecouldevenwritethatBisa strictsubsetofC.Now,wecouldalsoreverse thewaywewritethis.Andthenwe'rereallyjust talkingaboutsupersets.Sowecouldreverse thisnotation,andwecouldsaythat AisasupersetofB,andthisisjustanotherwayof sayingthatBisasubsetofA.Butthewayyoucould thinkaboutthisis,Acontainsevery elementthatisinB.Anditmightcontainmore.Itmightcontain exactlyeveryelement.Soyoucankindofview thisasyoukindofhavetheequalssymbolthere.Ifyouweretoviewthis asgreaterthanorequal.They'renotequite exactlythesamething.Butweknowalready thatwecouldalsowritethatAisastrict supersetofB,whichmeansthatAcontains everythingBhasandthensome.AisnotequivalenttoB.So hopefullythisfamiliarizesyouwiththenotionsofsubsetsand supersetsandstrictsubsets.UniversalsetandabsolutecomplementBringingthesetoperationstogetherUpNextBringingthesetoperationstogether