GATE CS 2003 Q30 — Relational Model: Relational Algebra

To translate the given SQL query into a relational algebra expression, we can map each SQL clause to its corresponding relational algebra operator:

1. The FROM clause (from $r_1, r_2, e_m$): In SQL, listing multiple relations separated by commas in the FROM clause performs a Cartesian product (cross product) of those relations. $$\text{Cartesian Product} = r_1 \times r_2 \times \dots \times r_m$$
2. The WHERE clause (where P): The WHERE clause filters the rows based on the predicate $P$. This corresponds to the selection operator ($\sigma$) in relational algebra. $$\sigma_P(r_1 \times r_2 \times \dots \times r_m)$$
3. The SELECT DISTINCT clause (Select distinct $a_1, a_2, e_n$): The SELECT clause specifies which attributes to project. Since relational algebra operates on sets, the projection operator ($\Pi$) automatically eliminates duplicates, matching the behavior of SELECT DISTINCT. $$\Pi_{a_1, a_2, \dots, a_n} \left( \sigma_P \left( r_1 \times r_2 \times \dots \times r_m \right) \right)$$

Combining these steps, the equivalent relational algebra expression is:

Thus, Option A is the correct choice.