For each of the following pairs of expressions give instances
For each of the following pairs of expressions, give instances of relations that show the expressions are not equivalent.
a. ΠA(R − S) and Π A (R) – ΠA (S)
b. σB < 4(AGmax(B)(R)) and AGmax(B)(σB<4(R))
c. In the preceding expressions, if both occurrences of max were replaced by min would the expressions be equivalent?
d. (R Θ S) Θ T and R Θ (S Θ T)
In other words, the natural left outer join is not associative.
e. σθ (E1 Θ E2) and E1 Θ σθ (E2), where θ uses only attributes from E2
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