What is the optimized version of the relation algebra expression…

GATE · 2014 · CS · Set 3 · Computer Science & IT

What is the optimized version of the relation algebra expression πA1(πA2(σF1(σF2(r))))\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r)))) where A1,A2A1, A2 are sets of attributes in rr with A1⊂A2A1 \subset A2 and F1,F2F1,F2 are Boolean expressions based on the attributes in rr ?

  1. A.

    πA1(σ(F1∧F2)(r))\pi_{A1}(\sigma_{(F1 \wedge F2)}(r))

  2. B.

    πA1(σ(F1∨F2)(r))\pi_{A1}(\sigma_{(F1 \vee F2)}(r))

  3. C.

    πA2(σ(F1∧F2)(r))\pi_{A2}(\sigma_{(F1 \wedge F2)}(r))

  4. D.

    πA2(σ(F1∨F2)(r))\pi_{A2}(\sigma_{(F1 \vee F2)}(r))

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