Proper Subset | Super Set | Power Set | Universal Set Subset

If A and B are two sets, then A is called the proper subset of B if A ⊆ B but B ⊇ A i.e., A ≠ B. The symbol '⊂' is used to denote proper subset. Subset DefinitionofSubset:IfAandBare twosets,andeveryelementofsetAisalsoanelementofsetB,thenA iscalledasubsetofBandwewriteitasA⊆BorB⊇AThesymbol ⊂ standsfor‘isasubsetof’or‘iscontainedin’ • Everysetisasubsetofitself,i.e.,A⊂A,B⊂B. • Emptysetisasubsetofeveryset. • Symbol‘⊆’isusedtodenote‘isasubsetof’or‘iscontainedin’. • A⊆BmeansAisasubsetofBorAiscontainedinB. • B⊆AmeansBcontainsA.  Forexample;1. LetA={2,4,6} B={6,4,8,2} HereAisasubsetofBSince,alltheelementsofsetAarecontainedinsetB. ButBisnotthesubsetofA Since,alltheelementsofsetBarenotcontainedinsetA. Notes:IfACBandBCA,thenA=B,i.e.,theyareequalsets. Everysetisasubsetofitself. Nullset or ∅ isasubsetofeveryset. 2. ThesetNofnaturalnumbersisasubsetofthesetZofintegersandwewriteN⊂Z. 3. LetA={2,4,6}B={x:xisanevennaturalnumberlessthan8}HereA⊂BandB⊂A. Hence,wecansayA=B 4. LetA={1,2,3,4} B={4,5,6,7} HereA⊄BandalsoB⊄C [⊄ denotes‘notasubsetof’] SuperSet:WheneverasetAisasubsetofsetB,wesaytheBisasupersetofAandwewrite,B⊇A. Symbol⊇isusedtodenote‘isasupersetof’ Forexample;A={a,e,i,o,u} B={a,b,c,.............,z}HereA⊆Bi.e.,AisasubsetofBbutB⊇Ai.e.,BisasupersetofA ProperSubset: IfAandBaretwosets,thenAiscalledthepropersubsetofBifA⊆BbutB⊇Ai.e.,A≠B.Thesymbol‘⊂’isusedtodenotepropersubset.Symbolically,wewriteA⊂B. Forexample; 1.A={1,2,3,4} Heren(A)=4 B={1,2,3,4,5} Heren(B)=5 Weobservethat,alltheelementsofAarepresentinBbuttheelement‘5’ofBisnotpresentinA. So,wesaythatAisapropersubsetofB. Symbolically,wewriteitasA⊂B Notes: Nosetisapropersubsetofitself. Nullsetor∅isapropersubsetofeveryset. 2.A={p,q,r} B={p,q,r,s,t} HereAisapropersubsetofBasalltheelementsofsetAareinsetBandalsoA≠B. Notes: Nosetisapropersubsetofitself. Emptysetisapropersubsetofeveryset. PowerSet: ThecollectionofallsubsetsofsetAiscalledthepowersetofA.ItisdenotedbyP(A).InP(A),everyelementisaset. Forexample; IfA={p,q}thenallthesubsetsofAwillbe P(A)={∅,{p},{q},{p,q}} NumberofelementsofP(A)=n[P(A)]=4=22 Ingeneral,n[P(A)]=2mwheremisthenumberofelementsinsetA. UniversalSet Asetwhichcontainsalltheelementsofothergivensetsiscalledauniversalset.Thesymbolfordenotingauniversalsetis∪orξ. Forexample; 1.IfA={1,2,3}   B={2,3,4}   C={3,5,7} thenU={1,2,3,4,5,7} [HereA⊆U,B⊆U,C⊆UandU⊇A,U⊇B,U⊇C] 2.IfPisasetofallwholenumbersandQisasetofallnegativenumbersthentheuniversalsetisasetofallintegers. 3.IfA={a,b,c}   B={d,e}   C={f,g,h,i} thenU={a,b,c,d,e,f,g,h,i}canbetakenasuniversalset. ●SetTheory●Sets ●Objects FormaSet ●Elements ofaSet ●Properties ofSets ●RepresentationofaSet ●DifferentNotationsinSets ●StandardSetsofNumbers ●Types ofSets ●Pairs ofSets ●Subsets ofaGivenSet ●Operations onSets ●Union ofSets ●Intersection ofSets ●Difference oftwoSets ●Complement ofaSet ●Cardinalnumberofaset ●CardinalPropertiesofSets ●Venn Diagrams 7thGradeMathProblems FromSubsettoHOMEPAGE New!CommentsHaveyoursayaboutwhatyoujustread!Leavemeacommentintheboxbelow.AskaQuestionorAnsweraQuestion. Didn'tfindwhatyouwerelookingfor?Orwanttoknowmoreinformation aboutMathOnlyMath. UsethisGoogleSearchtofindwhatyouneed. Sharethispage: What’sthis? FacebookTwitterPinterestWhatsAppMessenger HomeMathBlogPreschoolActivitiesKindergartenMath1stGradeMath2ndGradeMath3rdGradeMath4thGradeMath5thGradeMath6thGradeMath7thGradeMath8thGradeMath9thGradeMath10thGradeMath11&12GradeMathAlgebra1ConceptsofSetsMatrixProbabilityStatisticsLogarithmsBooleanAlgebraMathColoringPagesMultiplicationTableCoolMathsGamesMathFlashCardsOnlineMathQuizMathPuzzlesBinarySystemMathDictionaryConversionChartHomeworkSheetsMathProblemAnsFreeMathAnswersPrintableMathSheetFunnyMathAnswersEmploymentTestMathPatternsLinkPartnersAboutUsContactUsSiteMap [?]SubscribeToThisSite E-mailAddress FirstName Then Don'tworry—youre-mailaddressistotallysecure. IpromisetouseitonlytosendyouMathOnlyMath. ©and™math-only-math.com.AllRightsReserved.2010-2021.