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Equivalence Rules 1.Conjunctive selection operations can be deconstructed into a sequence of individual selections. o le,(E)=Oe (o,(E)) 2.Selection operations are commutative. o6(o4,(E)=04,(oa(E) 3.( Only the last in a sequence of projection operations is needed,the others can be omitted. Πz(Π,(.(n(E).…)=Π(E) 4.Selections can be combined with Cartesian products and theta joins. a.( a(E1XE2)=E1凶9E2 b.( 01(E1凶92E2)=E1M1A2E2 Database System Concepts-6th Edition 1.8 @Silberschatz,Korth and SudarshanDatabase System Concepts - 6 1.8 ©Silberschatz, Korth and Sudarshan th Edition Equivalence Rules 1. Conjunctive selection operations can be deconstructed into a sequence of individual selections. 2. Selection operations are commutative. 3. Only the last in a sequence of projection operations is needed, the others can be omitted. 4. Selections can be combined with Cartesian products and theta joins. a.  (E1 X E2 ) = E1  E2 b. 1 (E1 2 E2 ) = E1 1 2 E2 ( ( )) ( ( )) 1 2 2 1 sq sq E =sq sq E ( ) ( ( )) 1 2 1 2 sq Ùq E =sq sq E ( ( ( ( )) )) ( ) 1 2 1 L L  Ln E  = L E
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