Transformation of Relational Expressions Two relational algebra expressions are said to be equivalent if the two expressions generate the same set of tuples on every lega/database instance Note:order of tuples is irrelevant we don't care if they generate different results on databases that violate integrity constraints In SQL,inputs and outputs are multisets of tuples Two expressions in the multiset version of the relational algebra are said to be equivalent if the two expressions generate the same multiset of tuples on every legal database instance. An equivalence rule says that expressions of two forms are equivalent Can replace expression of first form by second,or vice versa Database System Concepts-7th Edition 16.8 ©Silberscha乜，Korth and SudarshanDatabase System Concepts - 7 16.8 ©Silberschatz, Korth and Sudarshan th Edition Transformation of Relational Expressions ▪ Two relational algebra expressions are said to be equivalent if the two expressions generate the same set of tuples on every legal database instance • Note: order of tuples is irrelevant • we don’t care if they generate different results on databases that violate integrity constraints ▪ In SQL, inputs and outputs are multisets of tuples • Two expressions in the multiset version of the relational algebra are said to be equivalent if the two expressions generate the same multiset of tuples on every legal database instance. ▪ An equivalence rule says that expressions of two forms are equivalent • Can replace expression of first form by second, or vice versa