Theory of Multivalued Dependencies Let D denote a set of functional and multivalued dependencies.The closure D+of D is the set of all functional and multivalued dependencies logically implied by D. Sound and complete inference rules for functional and multivalued dependencies: ·Reflexivity rule.If a is a set of attributes and B,then a→阝 holds. Augmentation rule.If a->B holds and y is a set of attributes, then y a-→yβholds.. ·Transitivity rule.lfa→B holds and B→holds,then a→y holds. Database System Concepts-7th Edition 28.3 ©Silberscha乜，Korth and SudarshanDatabase System Concepts - 7 28.3 ©Silberschatz, Korth and Sudarshan th Edition Theory of Multivalued Dependencies ▪ Let D denote a set of functional and multivalued dependencies. The closure D+ of D is the set of all functional and multivalued dependencies logically implied by D. ▪ Sound and complete inference rules for functional and multivalued dependencies: • Reflexivity rule. If  is a set of attributes and   , then  →  holds. • Augmentation rule. If  →  holds and  is a set of attributes, then   →   holds. • Transitivity rule. If  →  holds and  → holds, then  →  holds