Database Systems: Relational Algebra

Relational Algebra

• Relational algebra operations work on one or more relations to define another relation without changing the original relations.
• Both operands and results are relations, so output from one operation can become input to another operation.
• Allows expressions to be nested, just as in arithmetic, which is called closure property.

Basic Operations on Relations

• Selection: selects tuples that satisfy the given condition.
• Projection: returns its argument relation with specific attributes left out and removes duplicate rows.
• Union: combines two or more relations.
• Difference: returns the set of elements contained in one relation but not in another.
• Cartesian Product: associates every tuple of one relation with every tuple of another relation.
• Joins: combines two or more relations based on some conditions.

Select Operation

• Represented with the lower case letter Sigma (σ).
• Selects tuples that satisfy the given condition.
• The input relation to the select operation is only one.

Project Operation

• Represented with the letter π.
• Returns its argument relation with specific attributes left out.
• Removes duplicate rows.

Union Operation

• Combines two or more relations.
• Relations must be union compatible (or type compatible).

Set Difference Operation

• Returns the set of elements contained in one relation but not in another.
• Relations must be union compatible (or type compatible).

Set Intersection Operation

• Returns the set of elements common to both relations.
• Relations must be union compatible (or type compatible).

Cartesian Product Operation

• Associates every tuple of one relation with every tuple of another relation.
• Denoted by a cross symbol.
• Notation: r x s (all possible pairing).

Rename Operator

• It is a unary operator (input is a single relation).
• It is used to give the name of our choice to a new relation obtained after using any linear algebra operation.
• Notation: ρ (R,E).

Division Operator

• Used to find the tuples that are associated with every tuple of another relation.
• Notation: A/B or A ÷ B.
• Can be applied if and only if the attributes of B are a subset of A.

Join Operation

• Combines two or more relations based on some conditions.
• It is a combination of Cartesian product and selection process.
• Join types: Inner Join, Outer Join (Left, Right, Full), Theta Join, Equijoin, Natural Join.

Learn about relational algebra operations that work on one or more relations to define another relation, and how they can be nested like arithmetic expressions.