     11 

         

    11.1.  

              
     - ()  (..  
 ,        
).         
     (4  5).    ,  
 4       , 
     .  
    5     , 
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   .    ,    
     ,    
,    9.        
  ,        . 
             
    .    
       ,  
   . 

    11.2.       

        UCTX (.. ,   
  1),     ,   
 (. 11.1).        
 (COURSE), a     (TEACHERS)   
 (TEXTS) ( . 11.1    ).   
,        
      . , 
         
   .  , ,    
   ,      
    .  ,    ,  
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      . 
           
 .  ,  ,   
      (  
   COURSE -> COURSE).    
    

     11.     	309 

            
   .      
    "" ,    
   . 11.1  ,   . 11.2. 

    UCTX 
    COURSE	TEACHERS	TEXTS 

    Physics	Prof. Green	Basic Mechanics 
    Prof. Brown	Principles of Optics 
    Math	Prof . Green	Basic Mechanics 
    Vector Analysis 
    Trigonometry 
    
    . 11.1.    UCTX 

     

    COURSE	TEACHER	TEXT 
    Physics	Prof . Green	Basic Mechanics 
    Physics	Prof . Green	Principles of Optics 
    Physics	Prof. Brown	Basic Mechanics 
    Physics	Prof . Brown	Principles of Optics 
    Math	Prof. Green	Basic Mechanics 
    Math	Prof. Green	Vector Analysis 
    Math	Prof. Green	Trigonometry 
    
    
    . 11.2.      

          ,  
 {COURSE:c, TEACHER:/, TEXT:*}       
 ,      t    
, ,        
       ,  
,       : 
    IF         (c,tl,xl), (c,t2,x2) 
    THEN        (c,tl,x2), (c,t2,xl) 
    (        
    .) 
    ,        
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  ,       , 
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,     ,   " ". 
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      -; 
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       .  
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    .  ,    
        (  
   4). 

    310  III.    

      ""    ,   
 ,    .  ,   
 ,  :    ,    
     .  ,   
,       ,   
    {COURSE, TEACHER}  {COURSE, TEXT},  
 . 11.3.    " "    ; 
 ,         
           . 
   1971        
(Fagin)         . 

    			CX 

    COURSE	TEACHER		COURSE	TEXT 

    Physics Physics Math	Prof. Green Prof . Brown Prof. Green		Physics Physics 

Math Math Math	Basic Mechanics Principles of Optics Basic Mechanics Vector 

Analysis Trigonometry 
    
    
    
    
    . 11.3.      

    .  ,       
,      .  ,   
     :    
        
 .      
 UCTX     : UCT (  
     )  UCX ( 
      ).   
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,  ,    . 
            
 ,   . 11.3, , , , 
          
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 ).         
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  ).       : 

    COURSE - TEACHER COURSE - TEXT 

        ,      
  ,  "    "  "   ". 
         ,     
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..     COURSE -> TEACHER,   
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 (      ). ,   
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     11.      311 

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     : 

      -      |   . 

            : 

    COURSE   -    TEACHER  |   TEXT 

        ,     
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 . 
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 . 
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 R{A, , }.  R      {, }  
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  -  | . 
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    312	 III.    

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}  {, },     {, }  {, }.    , 
       
      . 

    11.3.       

              ,  
        
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  ,       
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    .      ,  
   "- "   >2. 
 ,           
,       .  , 
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 "2-". 
    .   -     
 (Aho),  (Beeri)   (Ullman) [11.1],     = 
    (Nicolas) [11.20]. 
         SPJ,   . 11.4 ( 
      ,    
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",       
     4.       
  SP, PJ  JS  SPJ,    SP 
 PJ   #,    ,     JS 
   (J#, S#).  ,     
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) ,         . 
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 ,      ,  
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  ). 

     11.     	313 

     . 11.4     ,  
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 SPJ          
, .. ,      
  .    ,     
,   ,   " SPJ  
   SP, PJ  JS"   : 

    IF		(sl,pl)	   SP 
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    AND		(jl,sl)	   JS 
    THEN		(sl,pl,jl)	   SPJ 
    
    
    SPJ		S#		#		J# 
    S1 S1 S2 S1		1 2 1 1		J2    
    
    
    PJ .  # I 
    SP I S#|  	#1				
I P#		J#			JS 1  J#l S#| 
    S1      S1      S2     	 2 1				1 2 1		J2  			
J2     S1      S1 
     52 
    I __ SPJ  	 *   				      
  J#,S# I 
    S#	#	J# 
    S1 S1 S2  -    S2 S1	1 2 1 1 1	J2   J2  
    original SPJ 
    
    
    . 11.4.  SPJ      , 
    

     ,  ,   (sl,pljl)    
 SP, PJ  JS. ( , ..   (sl,pl,jl) 
   SPJ, , ,  (si ,pl)   
 SP,      SPJ  .) 
         ,   (si, pi)   
 SP    ,   (sl,pl,j2)   
 SPJ   /2;    (pl,jl)  (/, 
si).         , 
   SPJ: 

    IF    (sl,pl,j2), (s2,pl,jl), (sl,p2,jl)    SPJ THEN   
(sl,pl,jl)            SPJ 

        , ..     
 SPJ,         (  
 )    .    
    ("  si   ! ! 
 ', '    si,  sl,pl iijl     
")!   -  >2    , 
     . 
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    314  III.    

    )    , 
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       ,        
  , ,..., Z. 
    ,      SP  
 {S#, P#}    SPJ   
  PJ  JS,   SPJ   
  *(SP, PJ, JS). 
     ,   SPJ    *(SP, PJ, JS) 
  3-.      ? 
  , ,    SPJ   
 ,      3-. 
      . 11.5.  
         3-. 

    SPJ					SPJ 
    S#	#	J#			S#	#	J# 
    S1	1	J2			S1	1	J2 
    S1	2			          	S1 S2 S1	2 1 1	   

             (S2,P1,J1),      
 (S1,P1,J1) 
    S2,P1,J1)       
               					       
  (S1,P1,J1),         ( ?) 

    . 11.5.        SPJ 

        (    ),  R{A, 
, }          {, }  
{, }    ,    R    
         
    . 

     11.      315 

           : 
       R{A, , }    *(, ) 
   ,         
\ . 
            
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     ).  
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).  ,  SPJ    5,   
  3-      
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      . 
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  (    10)    S   
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 ,   

    *   (   {  S#,   SNAME,   STATUS  },   {  S#,   CITY }   }. 

    316	 IN.    

     ,   S      
 {S#, SNAME, STATUS}  {S#, CITY},      
     . (,    , 
   .)     
 ( )  ,  S#    ( 
      [10.4]). ,  S 
     : 

    * ( { S#, SNAME }, { S#, STATUS }, { SNAME, CITY } ). 

         ,   , S#  SNAME, 
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   . 

    11.4.     

             
,     .    R, 
   1 (        
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 ).        
   R    ,   
     R,   . 
   

     11.     	317 

          ,   
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      2. 
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    2.   ,  (      [11.9]) 
      , 4 
 . 
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,         
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    3.   ,      : 
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        ; 
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  ; 
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(      )   ,   
 

    318	 III,    

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      5),     
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 , ..      ,    
 . 
             
  ,        . 
      ,     
        
   . 

    11.5.    

         ,   
    10  ,        
  .   ,        


     11.     	319 

               
        (   
)    .    
    ,      
     .   , 
        80-     
[10.12].          , 
    1. -    .     
 [11.10] ,       ,   
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.   ,   R     
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      . (  
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 ). 
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   ).        
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   .) 
           
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  ,   ,   
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"-"  , ,   
   -  . 
(,   [11.9]  5 - 
 ,      

    320	 III.    

     ,        .) 
          
,          [11.26],  
     (3,3). ,  
  (3,3)    ,      
4,      4     (3,3).  
,    ,     (3,3)  
      4 ( 5).     
   [ 11.9, 11.17]. 

    11.6.  

            
 ,    , 
   ,    
.         . 
        R{A, , }     -   
   ,    ,   
 (, ),     ,     
 ,    (, ),     
 .          
 {, }  {, },       
     ( ). 
        R{A, ,..., Z}    *(, 
,..., Z)    ,        
 , ,..., Z.     ()   
     . 
       4,    , 
  ,   , 
  .    5 ( 
 -  )    , 
   ,   , 
  ,   . 
   (  )   
        . 
               
        
    . 
       ,       
 .   ,    , 
,          
     ,   
      .     
        . 

     

    11.1.  ї   ,   R{A, } ,  
 (, )   R    ,    b  . 
    ,     
  R1       ? 
    11.2.         
,      .  

     11.     	
    321 11      


            ,   
     . ,  
      ,    
     .  
     ,      
           .   
      ,    . 
  ,      . 
    11.3.    . 10.3   10      
   R        . 
    ,     ,  
  4. 
    11.4. (  . 11.2).     
    ,    
  .         
 ,        
. ,      
  ,        
 .        
 ,          
.  ,   R     
 ,      ,   R   
  ,  R    .   , 
     . 

      

    11.1. Aho A.V., Beeri ., Ullman J. D. The Theory of Joins in Relational 
Databases // ACM TODS. 1979. 4,  3. (   Proc. 19th IEEE 
Symposium on Foundations of Computer Science.  1977.) 
       ,     ,  
    .       
 ,       
     (   
  [11.2]).    ,    
        
.         
,      ,  . 
    11.2. Beeri ., Fagin R., Howard J.H. A Complete Axiomatization for 
Functional and Multivalued Dependencies // Proc. 1977 ACM SIGMOD Intern. Conf. 
on Management of Data.  Toronto, Canada, 1977. 
          (Armstrong) 
[9.1],      ,    
.  ,         
   . 
    1.    .    , ,    
        ,       
 ,   - . 
    2.   .     ,   - . 

    322	 III,    

    3.  .         D,  AD  . 
    4.   .   -?/?-, - - . 
        ,    
  . 
    5.	.        D,    D-BC. 
    6.	.   -  - ,   - . 
    1.	.   - ,   -   ,  - -   - -. 
          ,     
        
   . 
    8.   .   -> ,   - . 
    9.   .    ,  > D, D   S,  
    ,    D. 
      (     9)   
 14, 8  9         
  . 
           ,  
   . 
    10.   -    -> ,   -> -. 
    11.3. Brosda V., Vossen G. Update and Retrieval Through a Universal Schema 
Interface // ACM TODS.  1988.  13,  4. 
    .   [11.14]. 
    11.4. Carlson C.R., Kaplan R.S. A Generalized Access Path Model and Its 
Application to a Relational Data Base System // Proc. 1976 ACM SIGMOD Intern. 
Conf. on Management of Data.  Washington, D.C., 1976. 
    .   [ 11.14]. 
    11.5. Date C.J. Will the Real Fourth Normal Form Please Stand Up? // C. J. 
Date and Hugh Darwen. Relational Database Writings 1989-1991. Reading, Mass.: 
Addison-Wesley, 1992. 
      ,        
  ,          
   (4).        . 
    11.6. Date C.J., Fagin R. Simple Conditions for Guaranteeing Higher Normal 
Forms in Relational Databases // Ibid. (    ACM TODS. 
 1992. 17, 3.) 
      ,    R      
   R  (..    ),  R 
   .  ,      
      ,   
 ,  , 4  ,  
   . 
    .      ,  :  
 R            
,   R    4,     . 
    11.7. Delobel ., Parker D.S. Functional and Multivalued Dependencies in a 
Relational Database and the Theory of Boolean Switching Functions. Tech. 
Report No. 142.  Dept. Maths. Appl. et Informatique, Univ. de Grenoble, 
France, 1978. 

     11.     	323 

       ,   [9.3],   
  . 
    11.8, Fagin R. Multivalued Dependencies and a New Normal Form for 
Relational Databases // ACM TODS.  1977.  2,  3. 
             
 4. 
           . 
,   ,    ,  
  DAYS,   ,   
   TEXT   TEACHER, 
     COURSE.    
 CTXD        . 

    CTXD 
    COURSE	TEACHER	TEXT	DAYS 
    Physics	Prof. Green	Basic Mechanics	5 
    Physics	Prof . Green	Principles of Optics	5 
    Physics	Prof. Brown	Basic Mechanics	6 
    Physics	Prof. Brown	Principles of Optics	4 
    Math	Prof . Green	Basic Mechanics	3 
    Math	Prof. Green	Vector Analysis	3 
    Math	Prof . Green	Trigonometry	4 

           {COURSE, TEACHER, 
TEXT}    : 

    { COURSE, TEACHER, TEXT } - DAYS. 

     ,      4,   
   ,     
  (   4  ).  
       ( TEACHER  
 COURSE   TEXT   COURSE).    
     R,      R 
 ""    > .   
      , 
         . 
       ,     
 ,    ,     
       .   
      (   
   4,    5),   DAYS     
  COURSE, TEACHER  TEXT,        
 -  .       
        
 (      ). 
    11.9. Fagin R. Normal Forms and Relational Database Operators // Proc. 
1979 ACM S1GMOD Intern. Conf. on Management of Data.  Boston, Mass., 1979. 
        -  
 ( 5).        
,    ""  , ..  
  ,      

    324  III.    

            . 
    11.10. Fagin R. A Normal Form for Relational Databases That Is Based on 
Domains and Keys // ACM TODS.  1981.  6,  3. 
    11.11. Fagin R. Acyclic Database Schemes (of Various Degrees): A Painless 
Introduction // IBM Research Report RJ3800. 1983. (: . 83 
8th Colloquium on Trees in Algebra and Programming: Springer-Verlag Lecture 
Notes in Computer Science No. 159 (eds. G. Ausiello and M. Protasi). New 
York, N.Y.: Springer-Verlag, 1983.) 
         ,     SPJ, 
    ,   
        . 
      (     
)  ,       
,       .   
, ,  .    
   ,  -     
 .           . 
    11.12. Fagin R., Vardi M.Y. The Theory of Data Dependencies A Survey// 
IBM Research Report RJ4321. 1984. (: Mathematics of Information 
Processing // Proc. Symposia in Applied Mathematics 34, American Mathematical 
Society, 1986.) 
              
 80-  (  ,   ""  
       ).  , 
           
       .     
 ,      . 
         
D     d,   d   D 
(     9.7).     
       [11.14]  [11.11] . 
    11.13. Fagin R., Mendelzon .., Ullman J.D. A Simplified Universal 
Relation Assumption and Its Properties // ACM TODS.  1982.  7,  3. 
         ,  " "   
      [11.14],  
         
 ,      . 
    11.14. Kent W. Consequences of Assuming a Universal Relation//Ibid.  
1981.  6, 4. 
          
 .       
,    ,    
 ,       
,   ,       
       "" 
.        ?  
 ,       ,     
.        [11.27],     
  [11.15]. 

     11.     	325 

      ,      , 
       
.        ( 
  )  :   
       ,     
 . , ,      , 
  "   ,    
 ": 

    RETRIEVE STATUS WHERE COLOR = 'Red' 

              . 
    1.     ,    -  
 ,       
  ( ,     ). 
 ,   [11.4] ( ,   ,  
 ,      
,   " "     ). 
         
.  , ,      ( 
 S  SP)     ;  ,  
      (  S   
)      .  -  
   ,        
 . 
    2.    ,  ,     
         
 ,       
  . 
        ,       
        
 (,       
  ), ,    
    ()  .   
  ,   : 

    RETRIEVE STATUS WHERE COLOR  'Red' 

       : "   ,  
   "  "   ,  
   "?        , 
      . ,   
        
: "   ,    
 ".        " 
 ,       ",  , 
,      (    
   S   ). 
    11.15. Kent W. The Universal Relation Revisited //ACM TODS.  1983.  8,  4. 
    11.16. Korth H.F. et al. System/U: A Database System Based on the 
Universal Relation Assumption // Ibid.  1984.  9,  3. 
           (data definition 
language  DDL),       
   ,   - . 

    326	 III.    

    11.17. Maier D., Ullman J.D. Fragments of Relations // Proc. 1983 SIGMOD 
Intern. Conf. on Management of Data.  San Jose, Calif, 1983. 
    11.18. Maier D., Ullman J.D., Vardi M.Y. On the Foundations of the 
Universal Relation Model // ACM TODS. 1984. 9, 2. (    
   "The Revenge of the JD"   Proc. 2nd ACM 
SIGFACT-SIGMOD Symposium on Principles of Database Systems.  Atlanta, Ga., 1983.) 
    11.19. Maier D., Ullman J.D. Maximal Objects and the Semantics of 
Universal Relation Databases//ACM TODS.  1983. 8,  1. 
            
,        
  (    [11.11]).   
     
 ,     .  
    ,       . 
    11.20. Nicolas J.M. Mutual Dependencies and Some Results on Undecomposable 
Relations // Proc. 4th Intern. Conf. on Very Large Data Bases.  Berlin, FOR, 1978. 
        " ",   
      ,  
    ,     
 (     ,     
).           
,    10. 
    11.21. Osborn S.L. Towards a Universal Relation Interface // Proc. 5th 
Intern. Conf. on Very Large Data Bases.  Rio de Janeiro, Brazil, 1979. 
      ,       
        
  ,        
 .       
 . 
    11.22. Parker D.S., Delobel . Algorithmic Applications for a New Result 
on Multivalued Dependencies // Ibid. 
         [11.7]    
,       . 
    11.23. Sagiv Y., Delobel ., Parker D.S., Fagin R. An Equivalence between 
Relational Database Dependencies and a Subclass of Propositional Logic // 
JACM.  
    1981. 28, 3. 
       [9.8]  [11.24]. 
    11.24. Sagiv Y., Fagin R. An Equivalence between Relational Database 
Dependencies and a Subclass of Propositional Logic // IBM Research Report 
RJ2500.  1979. 
       [9.8],    , 
   . 
    11.25. Sciore E. A Complete Axiomatization of Full Join Dependencies // JACM. 
    1982. 29, 2. 
       [11.2],    
,    . 
    11.26. Smith J.M. A Normal Form for Abstract Syntax // Proc. 4th Intern. 
Conf. on Very Large Data Bases.  Berlin, FOR, 1978. 

     11.     	327 

           (3,3). 
    11.27. Ullman J.D. On Kent's Consequences of Assuming a Universal Relation 
// ACM TODS.1983.8, 4. 
    11.28. Ullman J.D. The U.R.  Strikes Back // Proc.   1st ACM  
SIGFACT-SIGMOD Symposium on Principles of Database Systems.  Los Angeles, 
Calif, 1982. 

       

    11.1.    ,   R   
         ,  , 
    ,  S,  ,    
  .  ,  R    
 S    .    :  
R      R     
 R  .  , R    
 (   ,    
 ): 
    (   }    -       |   . 
      ,   R   
 *(, ) (,        
  ). 
     ,   R    4,    
 ( ),       
 . 
    .  R     : 
       -      |   {   } 
       -      |   {   } 
         ,  
        . 
    11.2.         
,      : 

    REPS      ( REP#, ... ) 
    PRIMARY KEY ( REP# ) AREAS     ( AREA#, . . . ) 
    PRIMARY KEY ( AREA* ) PRODUCTS  ( PRODS, ... ) 
    PRIMARY KEY ( PROD* ) 

             
 : 

    RA ( REP#, AREA* ) 
    PRIMARY KEY ( REP#, AREA# ) 

              

    RP ( REP#, PROD* ) 
    PRIMARY KEY { REP#, PROD# ) 

         --, 

    328	 III.    

        ,     
      (  
,    ,   
       ,  
  ).      
      ,   
          . 
   ,     "" 
  ( APR   ,    4). 
    11.3.          
       
  4.     : 0.   
 R       D. 
    1.      (    4)  D  
,    2  3. 
    2.    X -      , 
    4. 
    3.      D   ,  :   
 X  Y,      ,   . 
    11.4.   " ",   
   : 

    REPS	(  REP#,   ...   ) 
    PRIMARY KEY ( REP# ) 
    AREAS   ( AREA*, . . . ) 
    PRIMARY KEY ( AREA* ) 
    PRODUCTS; REP#, ... ) 
    PRIMARY KEY ( PROD# ) 
    RA     ( REP#, AREA* ) 
    PRIMARY KEY ( REP#, AREA# ) 
    RP     ( REP#, PROD# ) 
    PRIMARY KEY   (  REP#,   PRODtt   ) 
    AP        ( AREA*, PROD# ) 
    PRIMARY KEY ( AREAtt, PROD# ) 

       ,    RA, RP   
  " ". 

    330  III.    

