Theory of Multivalued Dependencies (Cont.) 4.Complementation rule.If a>>B holds,then a>>R-B-a holds. 5.Multivalued augmentation rule.If aB holds and y R and 8 sY,then y a>>δB holds. 6.Multivalued transitivity rule.If a>B holds and B>>y holds, then a->>y-βholds. 7.Replication rule.If a>B holds,then a>>B. 8.Coalescence rule.If a>>B holds and y B and there is a 8 such thatδR andδ∩β=☑andδ>Y,then a>y holds. Database System Concepts-7th Edition 28.16 @Silberschatz,Korth and SudarshanDatabase System Concepts - 7 28.16 ©Silberschatz, Korth and Sudarshan th Edition Theory of Multivalued Dependencies (Cont.) 4. Complementation rule. If   holds, then  R –  –  holds. 5. Multivalued augmentation rule. If   holds and   R and   , then     holds. 6. Multivalued transitivity rule. If   holds and   holds, then   –  holds. 7. Replication rule. If   holds, then  . 8. Coalescence rule. If   holds and    and there is a  such that   R and    =  and  , then   holds