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DEFINITION2.6.1CompatibleTablesTableRandSarecompatibleiftheyhavethesameheadings,withattributeschosenfromthesamedomainsandwiththesamemeanings.RSTheUnion,Intersection,andDifferenceOperationsOnlytablesthatarecompatiblecanbeinvolvedinUnion,Intersection,anddifferences.DEFINITION2.6.2Union,Intersection,andDifferenceLettableRandSarecompatible,whereHead(R)=Head(S)=A1…An.TheunionofRandSisthetableR∪S,withthesameheading,consistingofallrowsthatareinRorinSorinboth.Similarly,theIntersectionofRandSisthetableR∩S,consistingofthoserowsthatareinbothRandS.RSR∪SR∩S?RSR∪SRSR∩STheDifferenceofRandSisthetableR-S,consistingofallrowsthatappearinRbutdonotappearinS.RSR-SS-R?RSR-SAssignmentandAliasDuringevaluationofrelationalalgebraexpression,itissometimesusefultobeabletosavecertainintermediateresults.Wenextintroduceanotationmeanttoaddthiscapabilitytorelationalalgebra.DEFINITION2.6.3AssignmentandAliasLetRbeatableandletHead(R)=A1…An.AssumethatB1,…,BnarenattributessuchthatDomain(Bi)=Domain(Ai)foralli,1≤i≤n.WedefineanewtableS,whoseheadingisHead(S)=B1…Bn,bywritingtheassignmentS(B1,…,Bn):=R(A1,…,An).ThecontentofthenewtableSisexactlythesameasthecontentoftheoldtableR.Thesymbol:=usedinthisassignmentiscalledtheassignmentoperation.AliasS:=RWerefertoSasanaliasofthetableR.NotethatthetableRontherightcanresultfromanevaluationofrelationalalgebraexpression,andthusgivesusanopportunityto“save”intermediateresultsofevaluation,muchaswedowithassignmentstatementsusedinprogramminglanguage.ThetableSontheleftoftheassignmentoperationmustalwaysbeanamedtable,howeveritcannotbeanexpression.EXAMPLE2.6.3ConsiderthetablesRandS.Usingassignmentoperation,wecandefineanewtable:T:=(R∪S)-(R∩S)WecouldalsohavedefinethetableTbyfirstdefiningtwointermediatetables:T1:=(R∪S)T2:=(R∩S)T:=T1-T22.4relationaloperations.DEFINITION2.6.4ProductTheproductofthetablesRandSisatableTwhoseheadingisHead(T)=R.A1…R.AnS.B1…S.Bm.WesaytisarowinTifandonlyiftherearetworowsuinRandvinSsuchth