Relational Algebra

Based on Set Theory

Selection

• ${\sigma }_{predicate}(R)$ : (horizontal)
• SELECT * FROM R WHERE a_id = 'a2'

Projection

• $\Pi$ : retains only desired columns (vertical)
  Projection takes in a relation and outputs a relation with tuples that contain only specified attributes.
• SELECT b_id-100, a_id FROM R WHERE a_id = 'a2'

Union

• $S1\cap S2=S1-(S1-S2)$
• (SELECT * FROM R) UNION ALL (SELECT * FROM S)

Intersection

• (SELECT * FROM R) INTERSECT (SELECT * FROM S)

Difference

• (SELECT * FROM R) EXCEPT (SELECT * FROM S)

Product

• (SELECT * FROM R) CROSS JOIN (SELECT * FROM S)
• SELECT * FROM R, S

Join

Get tuples from both $r$ and $s$ and put on restriction $\theta$ on them.
$r{\bowtie }_{\theta }s={\sigma }_{\theta }(r\times s)$

• SELECT * FROM R JOIN S USING (ATTRIBUTE1, ATTRIBUTE2...)

• Natural Join

  • $R\bowtie S={\text{uppi}}_{unq}{\sigma }_{cond}(R\times S)$
  • Remove the duplicate column (Natural)