Chapter 4 — Quiz

13 questions. Answers and explanations at the bottom.

Multiple choice

Q1. Relational selection (σ) corresponds to which SQL clause? - A) The SELECT list - B) WHERE - C) JOIN - D) ORDER BY

Q2. Relational projection (π) corresponds to: - A) WHERE - B) The SELECT list (the columns chosen) - C) GROUP BY - D) LIMIT

Q3. A join (⋈) is equivalent to: - A) A projection followed by a selection - B) A Cartesian product followed by a selection on the matching condition - C) A union of two tables - D) A rename

Q4. If customers has 12 rows and orders has 15, customers CROSS JOIN orders returns: - A) 15 rows - B) 12 rows - C) 27 rows - D) 180 rows

Q5. "Closure" in relational algebra means: - A) Queries always terminate - B) Every operation takes relations as input and produces a relation as output - C) Tables are locked during queries - D) Duplicate rows are removed

Q6. Which property makes subqueries, CTEs, and views possible? - A) Three-valued logic - B) Closure (relations in, relations out) - C) Referential integrity - D) Bag semantics

Q7. "Customers who have never placed an order" is naturally expressed with: - A) Union (∪) - B) Intersection (∩) - C) Difference (−) / EXCEPT - D) Cartesian product (×)

Q8. SQL's SELECT list performs which algebra operation? - A) Selection (σ) - B) Projection (π) - C) Join (⋈) - D) Rename (ρ)

Q9. "Pushing selection down" means: - A) Sorting results before returning them - B) Filtering rows before an expensive join rather than after - C) Selecting fewer columns - D) Pushing data to disk

Q10. SQL operates on _ by default, while pure relational algebra operates on _. - A) sets / bags - B) bags (multisets) / sets - C) lists / sets - D) trees / graphs

Q11. Which removes duplicate rows? - A) UNION ALL - B) UNION - C) CROSS JOIN - D) Plain SELECT col

True/False

Q12. SQL's keyword SELECT performs relational selection (choosing rows). (True / False)

Q13. Two equivalent relational-algebra expressions always return the same relation, even if one is faster to compute. (True / False)

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Answer key

Q1 — B. Selection (σ) filters rows → WHERE.

Q2 — B. Projection (π) chooses columns → the SELECT list.

Q3 — B. Join = Cartesian product + selection on the join condition. This is why a missing condition yields a full product.

Q4 — D. 12 × 15 = 180. Every pairing, most meaningless — which is why you add a join condition.

Q5 — B. Closure: relations in, relations out. The result of any operation is itself a relation.

Q6 — B. Closure. Because a query returns a relation, you can query that — subqueries, CTEs, views.

Q7 — C. Difference: (all customers) − (customers who ordered) → EXCEPT (or an anti-join).

Q8 — B. Projection. (The name "SELECT" is a false friend — it's π, not σ.)

Q9 — B. Filter early, before the join, so the join processes fewer rows. A key optimizer rewrite.

Q10 — B. SQL = bags (duplicates allowed); pure algebra = sets (no duplicates).

Q11 — B. UNION dedupes; UNION ALL keeps duplicates (and is faster); CROSS JOIN and plain SELECT col keep duplicates.

Q12 — False. SQL's SELECT list is projection (π). Relational selection (σ) is the WHERE clause.

Q13 — True. Equivalence means identical results by definition; the optimizer relies on this to substitute a faster expression safely.

Scoring: 11–13 you see the algebra under the SQL — Part II will feel natural. 8–10 review the mapping table. Below 8, re-read "SQL is algebra in disguise" before Chapter 5.