Equivalence Rules (Cont.) 5.Theta-join operations (and natural joins)are commutative. E1凶gE2=E2凶9E1 6.(a)Natural join operations are associative: (E1凶E2)凶E3=E1凶(E2冈E3) (b)Theta joins are associative in the following manner: (E1凶01E2)凶923E3=E1凶01A03(E2凶92E3) where 02 involves attributes from only E2 and E3. Database System Concepts-6th Edition 1.9 @Silberschatz,Korth and SudarshanDatabase System Concepts - 6 1.9 ©Silberschatz, Korth and Sudarshan th Edition Equivalence Rules (Cont.) 5. Theta-join operations (and natural joins) are commutative. E1  E2 = E2  E1 6. (a) Natural join operations are associative: (E1 E2 ) E3 = E1 (E2 E3 ) (b) Theta joins are associative in the following manner: (E1 1 E2 ) 2 3 E3 = E1 1 3 (E2 2 E3 ) where 2 involves attributes from only E2 and E3