Exercise 15.6 Briefly answer the following questions:
1. Explain the role of relational algebra equivalences in the System R optimizer.
2. Consider a relational algebra expression of the form σc(πl(R × S)). Suppose that the equivalent expression with selections and projections pushed as much as possible, taking into account only relational algebra equivalences, is in one of the following forms. In each case give an illustrative example of the selection conditions and the projection lists (c, l, c1, l1, etc.).
(a) Equivalent maximally pushed form: πl1(σc1(R) × S).
(b) Equivalent maximally pushed form: πl1(σc1(R) × σc2(S)).
(c) Equivalent maximally pushed form: σc(πl1(πl2(R) × S)).
(d) Equivalent maximally pushed form: σc1(πl1( σc2(πl2(R)) × S)).
(e) Equivalent maximally pushed form: σc1(πl1(πl2(σc2(R)) × S)).
(f) Equivalent maximally pushed form: πl(σc1(πl1(πl2(σc2(R)) × S))).
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