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GATE Overflow Test Series | Databases | Test 1 | Question: 11

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Assume that relation $R$ is defined over the attribute set $A$ and relation $S$ is defined over the attribute set $B$ such that $B \subseteq A$. Let $C = A - B,$ that is, $C$ is the set of attributes of $R$ that are not attributes of $S.$ A division operator $R \div S$ defines a relation over the attributes $C$ that consists of the set of tuples from $R$ that match the combination of every tuple in $S.$ Which of the following relational algebra query is equivalent to $R \div S?$

  1. $\Pi_C(R) –  \Pi_C(\Pi_C(R) \times S) -R)$
  2. $\Pi_C(R) – \Pi_C(\Pi_C(R) \times S) -S)$
  3. $\Pi_C(R) – \Pi_A(\Pi_C(R) \times S) -S)$
  4. $\Pi_C(R) – \Pi_C(\Pi_B(S) \times R) -R)$
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$R \div S = \Pi_C(R) –\Pi_C(\Pi_C(R) \times S) -R)$
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