GATE CS 2021 Set 1 Q27 — Relational Model: Relational Algebra

To understand what the relational algebra expression generates, let us break it down step-by-step:

1. Renaming Operator:

   $\rho_{empNo1, age1}(empAge)$ creates a copy of the $empAge$ relation where the attributes are renamed to $empNo1$ and $age1$.

2. Theta-Join:

   The expression performs a theta-join between the original relation and the renamed relation:

   $$\text{empAge} \Join_{(age > age1)} \rho_{empNo1, age1}(\text{empAge})$$

   This join pairs an employee from the first relation with an employee from the second relation if and only if the first employee's age ($age$) is strictly greater than the second employee's age ($age1$).

3. Projection:

   $\Pi_{empNo}(\dots)$ projects the employee numbers ($empNo$) from the join result.

Analysis:

• An employee's tuple will appear in the join result if there exists at least one other employee in the company who is strictly younger than them (i.e., $age > age1$).
• The only employees who will not satisfy this condition are those who have the absolute minimum age in the company, as there is no employee younger than them.
• Therefore, the projection yields the employee numbers of all employees whose age is not the minimum.

Thus, the correct option is C.