Database System Concepts, 5th Ed.Silberschatz, Korth and SudarshanSee www.db-book.com for conditions on re-use Chapter 2: Relational ModelChapter 2: Relational ModelSilberschatz, Korth and Sudarshan 2.2 Database System Concepts - 5th Edition, Oct 5, 2006Chapter 2:Relational ModelChapter 2:Relational ModelStructure of Relational DatabasesFundamental Relational-Algebra-OperationsAdditional Relational-Algebra-OperationsExtended Relational-Algebra-OperationsNull ValuesModifcation of the DatabaseSilberschatz, Korth and Sudarshan 2.3 Database System Concepts - 5th Edition, Oct 5, 2006Example of a RelationExample of a RelationSilberschatz, Korth and Sudarshan 2.4 Database System Concepts - 5th Edition, Oct 5, 2006Basic StructureBasic Structure Formally, given sets D1, D2, . Dn a relation r is a subset of D1 xD2 x x DnThus, a relation is a set of n-tuples (a1, a2, , an) where each ai DiExample:Ifcustomer_name ={Jones, Smith, Curry, Lindsay, }/* Set of all customer names */customer_street ={Main, North, Park, } /* set of all street names*/customer_city ={Harrison, Rye, Pittsfeld, } /* set of all city names */Then r = {(Jones, Main,Harrison), (Smith,North, Rye), (Curry,North, Rye), (Lindsay, Park,Pittsfeld) } is a relation over customer_namexcustomer_streetxcustomer_citySilberschatz, Korth and Sudarshan 2.5 Database System Concepts - 5th Edition, Oct 5, 2006Attribute TypesAttribute TypesEach attribute of a relation has a nameThe set of allowed values for each attribute is called the domain of the attributeAttribute values are (normally) required to be atomic; that is, indivisibleE.g. the value of an attribute can be an account number, but cannot be a set of account numbersDomain is said to be atomic if all its members are atomicThe special value nullis a member of every domainThe null value causes complications in the defnition of many operationsWe shall ignore the efect of null values in our main presentation and consider their efect laterSilberschatz, Korth and Sudarshan 2.6 Database System Concepts - 5th Edition, Oct 5, 2006Relation SchemaRelation Schema A1, A2, , An are attributesR = (A1, A2, , An ) is a relation schemaExample:Customer_schema = (customer_name, customer_street, customer_city)r(R) denotes a relation r on the relation schema RExample:customer (Customer_schema)Silberschatz, Korth and Sudarshan 2.7 Database System Concepts - 5th Edition, Oct 5, 2006Relation InstanceRelation InstanceThe current values (relation instance) of a relation are specifed by a tableAn element t of r is a tuple, represented by a row in a tableJonesSmithCurryLindsaycustomer_nameMainNorthNorthParkcustomer_streetHarrisonRyeRyePittsfeldcustomer_citycustomerattributes(or columns)tuples(or rows)Silberschatz, Korth and Sudarshan 2.8 Database System Concepts - 5th Edition, Oct 5, 2006Relations are UnorderedRelations are Unordered Order of tuples is irrelevant (tuples may be stored in an arbitrary order) Example: account relation with unordered tuplesSilberschatz, Korth and Sudarshan 2.9 Database System Concepts - 5th Edition, Oct 5, 2006DatabaseDatabaseA database consists of multiple relationsInformation about an enterprise is broken up into parts, witheach relation storing one part of the informationaccount : stores information about accountsdepositor : stores information about which customerowns which account customer : stores information about customersStoring all information as a single relation such as bank(account_number, balance, customer_name, ..)results inrepetition of information e.g.,if two customers own an account (What gets repeated?)the need for null valuese.g., to represent a customer without an accountNormalization theory (Chapter 7) deals with how to design relational schemasSilberschatz, Korth and Sudarshan 2.10 Database System Concepts - 5th Edition, Oct 5, 2006The The customer customer RelationRelationSilberschatz, Korth and Sudarshan 2.11 Database System Concepts - 5th Edition, Oct 5, 2006The The depositor depositor RelationRelationSilberschatz, Korth and Sudarshan 2.12 Database System Concepts - 5th Edition, Oct 5, 2006KeysKeysLet K RK is a superkey of R if values for K are sufcient to identify a unique tuple of each possible relation r(R) by possible r we mean a relation r that could exist in the enterprise we are modeling.Example:{customer_name, customer_street} and {customer_name} are both superkeys of Customer, if no two customers can possibly have the same nameIn real life, an attribute such as customer_id would be used instead of customer_name to uniquely identify customers, but we omit it to keep our examples small, and instead assume customer names are unique.Silberschatz, Korth and Sudarshan 2.13 Database System Concepts - 5th Edition, Oct 5, 2006Keys (Cont.)Keys (Cont.)K is a candidate key if K is minimalExample:{customer_name} is a candidate key for Customer, since it is a superkey and no subset of it is a superkey.Primary key: a candidate key chosen as the principal means of identifying tuples within a relationShould choose an attribute whose value never, or very rarely, changes.E.g. email address is unique, but may changeSilberschatz, Korth and Sudarshan 2.14 Database System Concepts - 5th Edition, Oct 5, 2006Foreign KeysForeign KeysA relation schema may have an attribute that corresponds to the primary key of another relation.The attribute is called a foreign key.E.g. customer_name and account_number attributes of depositor are foreign keys to customer and account respectively.Only values occurring in the primary key attribute of the referenced relation may occur in the foreign key attribute of the referencing relation.Schema diagramSilberschatz, Korth and Sudarshan 2.15 Database System Concepts - 5th Edition, Oct 5, 2006Query LanguagesQuery LanguagesLanguage in which user requests information from the database.Categories of languagesProceduralNon-procedural, or declarativePure languages:Relational algebraTuple relational calculusDomain relational calculusPure languages form underlying basis of query languages that people use.Silberschatz, Korth and Sudarshan 2.16 Database System Concepts - 5th Edition, Oct 5, 2006Relational AlgebraRelational AlgebraProcedural languageSix basic operatorsselect: project: union: set diference: Cartesian product: xrename: The operators take one ortwo relations as inputs and produce a new relation as a result.Silberschatz, Korth and Sudarshan 2.17 Database System Concepts - 5th Edition, Oct 5, 2006Select Operation ExampleSelect Operation ExampleRelation rA B C D15122377310A=B ^ D > 5 (r)A B C D123710Silberschatz, Korth and Sudarshan 2.18 Database System Concepts - 5th Edition, Oct 5, 2006Select OperationSelect Operation Notation: p(r)p is called the selection predicateDefned as: p(r) = {t | t r and p(t)}Where p is a formula in propositional calculus consisting of terms connected by : (and), (or), (not)Each term is one of: op or where op is one of:=, , >, . 1200 (loan)loan_number (amount > 1200 (loan))Find the names of all customers who have a loan, an account, or both, from the bankcustomer_name (borrower) customer_name (depositor)Silberschatz, Korth and Sudarshan 2.31 Database System Concepts - 5th Edition, Oct 5, 2006Example QueriesExample QueriesFind the names of all customers who have a loan at the Perryridge branch.Find the names of all customers who have a loan at the Perryridge branch but do not have an account at any branch of the bank.customer_name (branch_name = Perryridge (borrower.loan_number = loan.loan_number(borrower x loan))) customer_name(depositor)customer_name (branch_name=Perryridge(borrower.loan_number = loan.loan_number(borrower x loan)))Silberschatz, Korth and Sudarshan 2.32 Database System Concepts - 5th Edition, Oct 5, 2006Example QueriesExample QueriesFind the names of all customers who have a loan at the Perryridge branch. Query 2 customer_name(loan.loan_number = borrower.loan_number ( (branch_name = Perryridge (loan)) xborrower))Query 1customer_name (branch_name = Perryridge (borrower.loan_number = loan.loan_number (borrower x loan)))Silberschatz, Korth and Sudarshan 2.33 Database System Concepts - 5th Edition, Oct 5, 2006Example QueriesExample QueriesFind the largest account balanceStrategy:Find those balances that are not the largestRename account relation as d so that we can compare each account balance with all othersUse set diference to fnd those account balances that were not found in the earlier step.The query is: balance(account) - account.balance(account.balance < d.balance (account x d (account)))Silberschatz, Korth and Sudarshan 2.34 Database System Concepts - 5th Edition, Oct 5, 2006Formal DefnitionFormal DefnitionA basic expression in the relational algebra consists of either one of the following:A relation in the databaseA constant relationLet E1 and E2be relational-algebra expressions; the following are all relational-algebra expressions: E1 E2 E1 E2 E1 x E2p (E1), P is a predicate on attributes in E1s(E1), S is a list consisting of some of the attributes in E1 x (E1), x is the new name for the result of E1Silberschatz, Korth and Sudarshan 2.35 Database System Concepts - 5th Edition, Oct 5, 2006Additional OperationsAdditional OperationsWe defne additional operations that do not add any power to therelational algebra, but that simplify common queries.Set intersectionNatural joinDivisionAssignmentSilberschatz, Korth and Sudarshan 2.36 Database System Concepts - 5th Edition, Oct 5, 2006Set-Intersection OperationSet-Intersection OperationNotation: r sDefned as:r s = { t | t r and t s }Assume: r, s have the same arity attributes of r and s are compatibleNote: r s = r (r s)Silberschatz, Korth and Sudarshan 2.37 Database System Concepts - 5th Edition, Oct 5, 2006Set-Intersection Operation ExampleSet-Intersection Operation ExampleRelation r, s:r sA B121A B23r sA B2Silberschatz, Korth and Sudarshan 2.38 Database System Concepts - 5th Edition, Oct 5, 2006Notation:r sNatural-Join OperationNatural-Join OperationLet r and s be relations on schemas R and S respectively. Then,r sis a relation on schema R S obtained as follows: Consider each pair of tuples tr from r and ts from s. If tr and ts have the same value on each of the attributes in R S, add a tuple tto the result, where t has the same value as tr on r t has the same value as ts on sExample:R = (A, B, C, D)S = (E, B, D)Result schema = (A, B, C, D, E)r s is defned as:r.A, r.B, r.C, r.D, s.E (r.B = s.B r.D = s.D (rxs))Silberschatz, Korth and Sudarshan 2.39 Database System Concepts - 5th Edition, Oct 5, 2006Natural Join Operation ExampleNatural Join Operation ExampleRelations r, s:A B12412C DaababB13123DaaabbErA B11112C DaaaabEsr sSilberschatz, Korth and Sudarshan 2.40 Database System Concepts - 5th Edition, Oct 5, 2006Division OperationDivision OperationNotation: Suited to queries that include the phrase for all.Let r and s be relations on schemas R and S respectively whereR = (A1, , Am , B1, , Bn )S = (B1, , Bn)The result ofr s is a relation on schemaR S = (A1, , Am)r s = { t|t R-S (r) u s ( tu r ) } Where tu means the concatenation of tuples t and u to produce a single tupler s Silberschatz, Korth and Sudarshan 2.41 Database System Concepts - 5th Edition, Oct 5, 2006Division Operation ExampleDivision Operation Example Relations r, s: r s:AB12A B12311134612rsSilberschatz, Korth and Sudarshan 2.42 Database System Concepts - 5th Edition, Oct 5, 2006Another Division ExampleAnother Division ExampleA BaaaaaaaaC DaabababbE11113111 Relations r, s: r s:DabE11A BaaCrsSilberschatz, Korth and Sudarshan 2.43 Database System Concepts - 5th Edition, Oct 5, 2006Division Operation (Cont.)Division Operation (Cont.)Property Let q = r sThen q is the largest relation satisfying q x s rDefnition in terms of the basic algebra operationLet r(R) and s(S) be relations, and let S Rr s = R-S (r ) R-S ( ( R-S (r ) x s ) R-S,S(r ))To see why R-S,S (r) simply reorders attributes of r R-S (R-S (r ) x s ) R-S,S(r) ) gives those tuples t in R-S (r ) such that for some tuple u s, tu r.Silberschatz, Korth and Sudarshan 2.44 Database System Concepts - 5th Edition, Oct 5, 2006Assignment OperationAssignment OperationThe assignment operation () provides a convenient way to express complex queries. Write query as a sequential program consisting ofa series of assignments followed by an expression whose value is displayed as a result of the query.Assignment must always be made to a temporary relation variable.Example:Write r s as temp1 R-S (r ) temp2 R-S ((temp1 x s ) R-S,S (r ))result = temp1 temp2The result to the right of the is assigned to the relation variable on the left of the .May use variable in subsequent expressions.Silberschatz, Korth and Sudarshan 2.45 Database System Concepts - 5th Edition, Oct 5, 2006Bank Example QueriesBank Example QueriesFind the names of all customers who have a loan and an account at bank.customer_name (borrower) customer_name (depositor)Find the name of all customers who have a loan at the bank and the loan amountcustomer_name, loan_number, amount (borrower loan)Silberschatz, Korth and Sudarshan 2.46 Database System Concepts - 5th Edition, Oct 5, 2006Query 1customer_name (branch_name = Downtown (depositoraccount )) customer_name (branch_name = Uptown (depositor account))Query 2 customer_name, branch_name (depositoraccount) temp(branch_name) ({(Downtown ), (Uptown )})Note that Query 2 uses a constant relation.Bank Example QueriesBank Example QueriesFind all customers who have an account from at least the Downtown and the Uptown branches.Silberschatz, Korth and Sudarshan 2.47 Database System Concepts - 5th Edition, Oct 5, 2006Find all customers who have an account at all branches located in Brooklyn city.Bank Example QueriesBank Example Queriescustomer_name, branch_name (depositor account) branch_name (branch_city = Brooklyn (branch))Silberschatz, Korth and Sudarshan 2.48 Database System Concepts - 5th Edition, Oct 5, 2006Extended Relational-Algebra-OperationsExtended Relational-Algebra-OperationsGeneralized ProjectionAggregate FunctionsOuter JoinSilberschatz, Korth and Sudarshan 2.49 Database System Concepts - 5th Edition, Oct 5, 2006Generalized ProjectionGeneralized ProjectionExtends the projection operation by allowing arithmetic functions to be used in the projection list.E is any relational-algebra expression Each of F1, F2, , Fn are are arithmetic expressions involving constants and attributes in the schema of E.Given relation credit_info(customer_name, limit, credit_balance), fnd how much more each person can spend: customer_name, limit credit_balance (credit_info)) ( ,..., ,2 1EnF F FSilberschatz, Korth and Sudarshan 2.50 Database System Concepts - 5th Edition, Oct 5, 2006Aggregate Functions and OperationsAggregate Functions and OperationsAggregation function takes a collection of values and returns a single value as a result.avg:average valuemin:minimum valuemax:maximum valuesum:sum of valuescount:number of valuesAggregate operation in relational algebra E is any relational-algebra expressionG1, G2 , Gn is a list of attributes on which to group (can be empty)Each Fi is an aggregate functionEach Ai is an attribute name) () ( , , ( ), ( , , ,2 2 1 1 2 1En n nA F A F A F G G G Silberschatz, Korth and Sudarshan 2.51 Database System Concepts - 5th Edition, Oct 5, 2006Aggregate Operation ExampleAggregate Operation ExampleRelation r:A BC77310 g sum(c) (r)sum(c )27Silberschatz, Korth and Sudarshan 2.52 Database System Concepts - 5th Edition, Oct 5, 2006Aggregate Operation ExampleAggregate Operation ExampleRelation account grouped by branch-name:branch_nameg sum(balance) (account)branch_nameaccount_number balancePerryridgePerryridgeBrightonBrightonRedwoodA-102A-201A-217A-215A-222400900750750700branch_name sum(balance)PerryridgeBrightonRedwood13001500700Silberschatz, Korth and Sudarshan 2.53 Database System Concepts - 5th Edition, Oct 5, 2006Aggregate Functions (Cont.)Aggregate Functions (Cont.)Result of aggregation does not have a nameCan use rename operation to give it a nameFor convenience, we permit renaming as part of aggregate operationbranch_nameg sum(balance) as sum_balance (account)Silberschatz, Korth and Sudarshan 2.54 Database System Concepts - 5th Edition, Oct 5, 2006Outer JoinOuter JoinAn extension of the join operation that avoids loss of information.Computes the join and then adds tuples form one relation that does not match tuples in the other relation to the result of the join. Uses null values:null signifes that the value is unknown or does not exist All comparisons involving null are (roughly speaking) false by defnition.We shall study precise meaning of comparisons with nulls laterSilberschatz, Korth and Sudarshan 2.55 Database System Concepts - 5th Edition, Oct 5, 2006Outer Join ExampleOuter Join ExampleRelation loanRelation borrowercustomer_nameloan_numberJonesSmithHayesL-170L-230L-155300040001700loan_number amountL-170L-230L-260branch_nameDowntownRedwoodPerryridgeSilberschatz, Korth and Sudarshan 2.56 Database System Concepts - 5th Edition, Oct 5, 2006Outer Join ExampleOuter Join ExampleJoin loanborrowerloan_number amountL-170L-23030004000customer_nameJonesSmithbranch_nameDowntownRedwoodJonesSmithnullloan_number amountL-170L-230L-260300040001700customer_name branch_nameDowntownRedwoodPerryridge Left Outer JoinloanborrowerSilberschatz, Korth and Sudarshan 2.57 Database System Concepts - 5th Edition, Oct 5, 2006Outer Join ExampleOuter Join Exampleloan_number amountL-170L-230L-15530004000nullcustomer_nameJonesSmithHayesbranch_nameDowntownRedwoodnullloan_number amountL-170L-230L-260L-155300040001700nullcustomer_nameJonesSmithnullHayesbranch_nameDowntownRedwoodPerryridgenull Full Outer Joinloanborrower Right Outer JoinloanborrowerSilberschatz, Korth and Sudarshan 2.58 Database System Concepts - 5th Edition, Oct 5, 2006Null ValuesNull ValuesIt is possible for tuples to have a null value, denoted by null, for some of their attributesnull signifes an unknown value or that a value does not exist.The result of any arithmetic expression involving null is null.Aggregate functions simply ignore null values (as in SQL)For duplicate elimination and grouping, null is treated like any other value, and two nulls are assumed to bethe same (as in SQL)Silberschatz, Korth and Sudarshan 2.59 Database System Concepts - 5th Edition, Oct 5, 2006Null ValuesNull ValuesComparisons with null values return the special truth value: unknownIf false was used instead of unknown, thennot (A < 5) would not be equivalent to A >= 5Three-valued logic using the truth value unknown:OR: (unknown or true) = true, (unknown or false)= unknown (unknown or unknown) = unknownAND: (true and unknown) = unknown, (false and unknown)= false, (unknown and unknown) = unknownNOT:(not unknown) = unknownIn SQL P is unknown evaluates to true if predicate P evaluates to unknownResult of selectpredicate is treated as false if it evaluates to unknownSilberschatz, Korth and Sudarshan 2.60 Database System Concepts - 5th Edition, Oct 5, 2006Modifcation of the DatabaseModifcation of the DatabaseThe content of the database may be modifed using the following operations:DeletionInsertionUpdatingAll these operations are expressed using the assignment operator.Silberschatz, Korth and Sudarshan 2.61 Database System Concepts - 5th Edition, Oct 5, 2006DeletionDeletionA delete request is expressed similarly to a query, except instead of displaying tuples to the user, the selected tuples are removed from the database.Can delete only whole tuples; cannot delete values on only particular attributesA deletion is expressed in relational algebra by:r r Ewhere r is a relation and E is a relational algebra query.Silberschatz, Korth and Sudarshan 2.62 Database System Concepts - 5th Edition, Oct 5, 2006Deletion ExamplesDeletion ExamplesDelete all account records in the Perryridge branch. Delete all accounts at branches located in Needham.r1 branch_city = Needham (accountbranch )r2 account_number, branch_name, balance (r1)r3 customer_name, account_number (r2 depositor)account account r2depositor depositor r3 Delete all loan records with amount in the range of 0 to 50loan loan amount 0and amount 50 (loan)account account branch_name = Perryridge (account )Silberschatz, Korth and Sudarshan 2.63 Database System Concepts - 5th Edition, Oct 5, 2006InsertionInsertionTo insert data into a relation, we either:specify a tuple to be insertedwrite a query whose result is a set of tuples to be insertedin relational algebra, an insertion is expressed by:r rEwhere r is a relation and E is a relational algebra expression.The insertion of a single tuple is expressed by letting Ebe a constant relation containing one tuple. Silberschatz, Korth and Sudarshan 2.64 Database System Concepts - 5th Edition, Oct 5, 2006Insertion ExamplesInsertion ExamplesInsert information in the database specifying that Smith has $1200 in account A-973 at the Perryridge branch.Provide as a gift for all loan customers in the Perryridge branch, a $200 savings account.Let the loan number serve as the account number for the new savings account.account account{(A-973, Perryridge, 1200)}depositor depositor{(Smith, A-973)}r1 (branch_name = Perryridge (borrowerloan))account account loan_number, branch_name, 200 (r1)depositor depositor customer_name, loan_number (r1)Silberschatz, Korth and Sudarshan 2.65 Database System Concepts - 5th Edition, Oct 5, 2006UpdatingUpdatingA mechanism to change a value in a tuple without charging all values in the tupleUse the generalized projection operator to do this task Each Fi is either the I th attribute of r, if the I th attribute is not updated, or,if the attribute is to be updated Fi is an expression, involving only constants and the attributes of r, which gives the new value for the attribute) (, , , ,2 1r rlF F F Silberschatz, Korth and Sudarshan 2.66 Database System Concepts - 5th Edition, Oct 5, 2006Update ExamplesUpdate ExamplesMake interest payments by increasing all balances by 5 percent.Pay all accounts with balances over $10,000 6 percent interest and pay all others 5 percent account account_number, branch_name, balance * 1.06 ( BAL > 10000 (account )) account_number, branch_name, balance * 1.05 (BAL 10000 (account))account account_number, branch_name, balance * 1.05 (account)Database System Concepts, 5th Ed.Silberschatz, Korth and SudarshanSee www.db-book.com for conditions on re-use End of Chapter 2End of Chapter 2Silberschatz, Korth and Sudarshan 2.68 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.3. The Figure 2.3. The branch branch relationrelationSilberschatz, Korth and Sudarshan 2.69 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.6: The Figure 2.6: The loanloan relationrelationSilberschatz, Korth and Sudarshan 2.70 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.7: The Figure 2.7: The borrowerborrower relationrelationSilberschatz, Korth and Sudarshan 2.71 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.9Figure 2.9Result of Result of branch_name = Perryridge (loan) Silberschatz, Korth and Sudarshan 2.72 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.10: Figure 2.10: Loan number and the amount of the loanLoan number and the amount of the loanSilberschatz, Korth and Sudarshan 2.73 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.11: Names of all customers who Figure 2.11: Names of all customers who have either an account or an loanhave either an account or an loanSilberschatz, Korth and Sudarshan 2.74 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.12: Figure 2.12: Customers with an account but no loanCustomers with an account but no loanSilberschatz, Korth and Sudarshan 2.75 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.13: Result of Figure 2.13: Result of borrower borrower |X| |X| loanloanSilberschatz, Korth and Sudarshan 2.76 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.14Figure 2.14Silberschatz, Korth and Sudarshan 2.77 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.15Figure 2.15Silberschatz, Korth and Sudarshan 2.78 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.16Figure 2.16Silberschatz, Korth and Sudarshan 2.79 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.17Figure 2.17Largest account balance in the bankLargest account balance in the bankSilberschatz, Korth and Sudarshan 2.80 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.18: Customers who live on the Figure 2.18: Customers who live on the same street and in the same city as same street and in the same city as SmithSmithSilberschatz, Korth and Sudarshan 2.81 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.19: Customers with both an Figure 2.19: Customers with both an account and a loan at the bankaccount and a loan at the bankSilberschatz, Korth and Sudarshan 2.82 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.20Figure 2.20Silberschatz, Korth and Sudarshan 2.83 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.21Figure 2.21Silberschatz, Korth and Sudarshan 2.84 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.22Figure 2.22Silberschatz, Korth and Sudarshan 2.85 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.23Figure 2.23Silberschatz, Korth and Sudarshan 2.86 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.24: The Figure 2.24: The credit_infocredit_info relationrelationSilberschatz, Korth and Sudarshan 2.87 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.25Figure 2.25Silberschatz, Korth and Sudarshan 2.88 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.26: The Figure 2.26: The pt_works pt_works relationrelationSilberschatz, Korth and Sudarshan 2.89 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.27Figure 2.27The The pt_workspt_works relation after regroupingrelation after regroupingSilberschatz, Korth and Sudarshan 2.90 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.28Figure 2.28Silberschatz, Korth and Sudarshan 2.91 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.29Figure 2.29Silberschatz, Korth and Sudarshan 2.92 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.30Figure 2.30The The employeeemployee and and ft_works relationsft_works relationsSilberschatz, Korth and Sudarshan 2.93 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.31Figure 2.31Silberschatz, Korth and Sudarshan 2.94 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.32Figure 2.32Silberschatz, Korth and Sudarshan 2.95 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.33Figure 2.33Silberschatz, Korth and Sudarshan 2.96 Database System Concepts - 5th Edition, Oct 5, 2006Figure 2.34Figure 2.34