Equivalence Rules (Cont.) 9.The set operations union and intersection are commutative EE2=E20E1 E1∩E2=E2∩E1 (set difference is not commutative). 10.Set union and intersection are associative. (E10E2)UE3=E10(E2E3) (E1∩E2)∩E3=E1∩(E2∩E3) 11.The selection operation distributes over and-. 0(E1-E2)=O(E)-0(E2) and similarly for and in place of Also: O6(E1-E2)=O(E1)-E2 and similarly for in place of -but not for 12.The projection operation distributes over union Π(E1UE2)=(Π(E1)U(Π(E2) Database System Concepts-6th Edition 1.13 ©Silberschat乜，Korth and SudarshanDatabase System Concepts - 6 1.13 ©Silberschatz, Korth and Sudarshan th Edition Equivalence Rules (Cont.) 9. The set operations union and intersection are commutative E1  E2 = E2  E1 E1  E2 = E2  E1 (set difference is not commutative). 10. Set union and intersection are associative. (E1  E2 )  E3 = E1  (E2  E3 ) (E1  E2 )  E3 = E1  (E2  E3 ) 11. The selection operation distributes over ,  and –.  (E1 – E2 ) =  (E1 ) –  (E2 ) and similarly for  and  in place of – Also:  (E1 – E2 ) =  (E1 ) – E2 and similarly for  in place of –, but not for  12. The projection operation distributes over union L (E1  E2 ) = (L (E1 ))  (L (E2 ))