Equivalence Rules 1.Conjunctive selection operations can be deconstructed into a sequence of individual selections. 01A2(E)三001(C2(E)》 2.Selection operations are commutative. 0,(C92(E)》三O2(C,(E) 3.Only the last in a sequence of projection operations is needed,the others can be omitted. Π(2(（ΠLn(E)…)》三ΠL,(E) here L1∈L2.∈Ln 4.Selections can be combined with Cartesian products and theta joins. a.09(E1XE2)≡E1☒9E2 b.091(E1凶02E2)三E1☒91A2E2 Database System Concepts-7th Edition 16.9 @Silberschatz,Korth and SudarshanDatabase System Concepts - 7 16.9 ©Silberschatz, Korth and Sudarshan th Edition Equivalence Rules 1. Conjunctive selection operations can be deconstructed into a sequence of individual selections. σ1  2 (E) ≡ σ1 (σ2 (E)) 2. Selection operations are commutative. σ1 (σ2 (E)) ≡ σ2 (σ1 (E)) 3. Only the last in a sequence of projection operations is needed, the others can be omitted.  L1 ( L2 (…( Ln (E))…)) ≡  L1 (E) where L1 ⊆ L2 … ⊆ Ln 4. Selections can be combined with Cartesian products and theta joins. a. σ (E1 x E2 ) ≡ E1 ⨝  E2 b. σ 1 (E1 ⨝2 E2 ) ≡ E1 ⨝ 1∧2 E2