Show that the following equivalences hold. Explain how you can apply then to improve the efficiency of
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Show that the following equivalences hold. Explain how you can apply then to improve the efficiency of certain queries:
a. E1 Θθ (E2 − E3) = (E1 Θθ E2 − E1 Θθ E3).
b. σθ (AGF (E)) = AGF (σθ (E)), where θ uses only attributes from A.
c. σθ (E1 Θ E2) = σθ(E1) Θ E2 where θ uses only attributes from E1.
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