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lec06.365

# lec06.365 - Fall 2007 CPE/CSC 365 Introduction to Database...

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. . Fall 2007 CPE/CSC 365: Introduction to Database Systems Alexander Dekhtyar . . Relational Algebra. Part 1. Definitions. Relational Algebra Notation R, T, S, . . . – relations. t, t 1 , t 2 , . . . – tuples of relations. t ( n ) – tuple with n attributes. t [1] , t [2] , . . ., t [ n ] – 1st, 2nd,. . . nth attribute of tuple t . t.name – attribute name of tuple t (attribute names and numbers are inter- changable ). R.name, R [1] , . . . – attribute name or attribute number 1 (etc.) of relation R . R ( X 1 : V 1 , . . . , X n : V n ) – relational schema specifying relation R with n attributes X 1 , . . . , X n of types V 1 , . . . , V n . We let V i specify both the type and the set of possible values in it. Base Operations Union Definition 1 Let R = { t } and S = { t } be two relations over the same rela- tional schema. Then, the union of R and S , denoted R S is a relation T , such that: T = { t ′′ | t ′′ R or t ′′ S } . Union of two relations combines in one relation all their tuples. Note: it is important to note that for union to be applicable to two relations R and S , they must have the same schema . 1

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Difference Definition 2 Let R and S be two relations over the same relational schema. Then, the difference of R and S , denoted R S is a relation T such that: T = { t | t R and t negationslash∈ S } . Difference of two relations R and S is a relation that contains all tuples from R that are not contained in S . Cartesian Product Definition 3 Let R and S be two relations. The cartesian product of R and S , denoted R × S is a relation T such that: T = { t | t = ( a 1 , . . . , a n , b 1 , . . . , b m ) ( a 1 , . . . , a n ) R ( b 1 , . . . , b m ) S } . Cartesian product “glues” together all tuples of one relation with all tuples of the other one. Selection Definition 4 Let database D consist of relations R 1 , . . . R n . Let X, Y be at- tributes of one of the relations R 1 , . . . R n . An atomic selection condition is an expression of one of the forms: X op α ; X op Y, where α V and V is X ’s domain; op ∈ { = , negationslash = , <, >, , ≥} and X and Y have comparable types. An atomic selection condition is a selection condition. Let C 1 and C 2 be two selection conditions. Then C 1 C 2 , C 1 C 2 and ¬ C 1 are selection conditions.
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lec06.365 - Fall 2007 CPE/CSC 365 Introduction to Database...

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