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What is the optimized version of the relation algebra expression πA1(πA2 (σF1 (σF2(r)))) , where A1, A2 are sets of attributes in r with A1 ⊂ A2 and F1, F2 are Boolean expressions based on the attributes in r?
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- πA1( σ(F1∧F2)(r))
- πA1( σ(F1∨F2)(r))
- πA2( σ(F1∧F2)(r))
- πA2( σ(F1∨F2)(r))
- πA1( σ(F1∧F2)(r))
Correct Option: A
ΠA1 (ΠA2 (σF1 (σF1 (r))))
= ΠA1 (ΠA2 (σ (F1 ∧ F2)(r)))
∴ A1 ⊂ A2 , final relation will be displaying values for attributes present in set A.
ΠA1 (σ (F1 ∧ F2)(r))