Relational Algebra & Joins

Question 1

If Table A has 5 rows and Table B has 4 rows, and you perform a CROSS JOIN (Cartesian Product), how many rows will be in the result set?

Accepted Answer

20 rows — cross join pairs every row in A with every row in B — A Cartesian Product matches every row in Table A with every row in Table B. 5 x 4 = 20 rows.

Question 2

Relational algebra is…

Accepted Answer

The formal theoretical base for SQL query language semantics — It defines operations on relations (tables); SQL queries are translated into relational-algebra expressions for execution/optimization.

Question 3

The SELECTION operation (σ) does what?

Accepted Answer

Filters rows by condition — Selection σ_condition(R) returns the tuples (rows) of R meeting the predicate — the horizontal filter.

Question 4

The PROJECTION operation (π) does what?

Accepted Answer

Selects only the named columns — Projection π_columns(R) keeps only the listed attributes — the vertical slice; pure relational projection also removes duplicate tuples.

Question 5

A JOIN (⋈) combines…

Accepted Answer

Rows from two tables on a matching key — Joins merge tuples from different tables where a join condition holds — the core of querying related, normalized data.

Question 6

An INNER join returns…

Accepted Answer

Only matching rows — Inner join keeps only tuples that satisfy the join condition on both sides; non-matching rows are excluded.

Question 7

A LEFT (outer) join returns…

Accepted Answer

All left-side rows, NULLs for unmatched right — Left outer join preserves every left-side tuple, filling unmatched right-side columns with NULLs — useful to keep all of one side.

Question 8

The CARTESIAN PRODUCT (×) of two relations produces…

Accepted Answer

Each row of A combined with each row of B — Cross product pairs each row of one relation with every row of the other; a join is a cross product followed by a selection.

Question 9

A theta join (⋈_θ) is a Cartesian product followed by…

Accepted Answer

A selection on condition θ — Conceptually, join = σ_θ(R × S): take all combinations, then keep those satisfying θ. An equijoin uses equality conditions.

Question 10

A NATURAL join joins on…

Accepted Answer

Matching column names — Natural join implicitly equates same-named attributes and outputs one copy of each shared column.

Users (A)
ID	Name
1	Alice
2	Bob
3	Eve

Orders (B)
U_ID	Item
1	Pen
2	Mug
9	Hat

Result
ID	Name	Item
1	Alice	Pen
2	Bob	Mug

σ, π or ⋈?

Test your knowledge

If Table A has 5 rows and Table B has 4 rows, and you perform a CROSS JOIN (Cartesian Product), how many rows will be in the result set?

The short version

In more depth

Relational Algebra

Core Operations

Join Types

Interview Questions

References & Further Reading

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