Show that the following equivalences hold Explain how you can apply then to improve the efficiency of certain queries a E 1 (E 2 E 3 ) (E 1 E 2 E 1 E 3 ) b (AG F (E)) A G F ( (E)), where uses only attributes from A c (E 1 E 2 ) (E 1 ) E 2 where uses only attributes from E 1

Question: Show that the following equivalences hold. Explain how you can apply then to improve the efficiency of certain queries: a. E 1 (E

Show that the following equivalences hold. Explain how you can apply then to improve the efficiency of certain queries:

a. E₁ Θ_θ (E₂ − E₃) = (E₁ Θ_θ E₂ − E₁ Θ_θ E₃).

b. σ_θ (AG_F (E)) = _AG_F (σ_θ(E)), where θ uses only attributes from A.

c. σ_θ (E₁ Θ E₂) = σ_θ(E₁) Θ E₂ where θ uses only attributes from E₁.

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a E Me E E3 E Me EE E3 Let us rename E EE3 as R E E as R and E E as R3 It is clear that if a tuple t belongs to R it will also belong to R If a tuple ... View full answer

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