Consider a join \(X_1 ⋈_ \theta X_2\). Let \(A_1\) and \(A_2\) be sets of attributes from \(X_1\) and \(X_2\)respectively. Let \(A_3\) be the attributes of \(X_1\) that are involved in join condition \(\theta\) but are not in \(A_1 \cup A_2\), and let \(A_4\) be attributes of \(X_2\) that are involved in join condition \(\theta\) but are not in \(A_1 \cup A_2\). What is the optimized version of the relational algebra expression \(\Pi _{A_1 \cup A_2}(X_1 ⋈_ \theta X_2)\)?
1
\(((\Pi _{A_1 \cup A_3}(X_1)) ⋈_ \theta (\Pi _{A_2 \cup A_4}(X_2))\)
2
\(\Pi _{A_3 \cup A_4}((\Pi _{A_1 \cup A_2}(X_1)) ⋈_ \theta (\Pi _{A_1 \cup A_2}(X_2)))\)
3
\(\Pi _{A_1 \cup A_2}((\Pi _{A_1 \cup A_3}(X_1)) ⋈_ \theta (\Pi _{A_2 \cup A_4}(X_2)))\)
4
\(((\Pi _{A_1 \cup A_2}(X_1)) ⋈_ \theta (\Pi _{A_3 \cup A_4}(X_2))\)