GATE CS 2000 Q1.23 — Relational Model: Relational Algebra

Basic relational algebra operations $(\sigma, \pi, \times, \Join, \cup, \cap, -)$ do not support aggregation functions such as SUM, AVG, COUNT, MIN, or MAX. These require the extended relational algebra operator (the grouping and aggregation operator, $\mathcal{G}$).

Let's analyze each option:

• Option A: Department address of every employee can be expressed as: $$\pi_{\text{name, address}}(\text{employee} \Join_{\text{dept-no}} \text{department})$$
• Option B: Employees whose name is the same as their department name can be expressed as: $$\sigma_{\text{name} = \text{dept-name}}(\text{employee} \Join_{\text{dept-no}} \text{department})$$
• Option C: The sum of all employees' salaries requires the aggregation operator $\mathcal{G}$ (i.e., $\mathcal{G}_{\text{sum}(\text{salary})}(\text{employee})$), which is not a basic relational algebra operation.
• Option D: All employees of a given department (e.g., department 'D101') can be expressed as: $$\sigma_{\text{dept-no} = \text{'D101'}}(\text{employee})$$

Therefore, the query in Option C cannot be expressed using basic relational algebra operations.