```
tags:
- Mathematics
```

A family of algebras with a well-founded semantics used for modelling the data stored in relational databases, and defining queries on it.

The primary operations of relational algebra:

- Set Operations
- Union(
): For , The union of two relations, it contains all the tuples of , or , or both, with duplicate tuples being eliminated. Both relations must be union-compatible.

For a union operation to be applied, the following rules must hold: and must have the same quantity of attributes.- Attribute domains must be compatible.
- Duplicate tuples get automatically eliminated.

- Set Intersect(
): Contains all the rows of frequent attributes from two relations. - Set different(
): For , it retrieves tuples in that are not in . - Cartesian product(
): Also called Cross-product, it combines two relations.

- Union(
- Relational Operations
- Select(
): It selects a sub-set of tuples that satisfy the given predicate from a relation. It is defined as , where stands for selection predicate, stands for relation, and is a propositional logic formula which may use connectors like*and*,*or*, and*not.* - Projection(
): The Projection operation works on a single relation R, selecting certain attributes and discarding other. Duplicate tuples are automatically eliminated. - Rename(
): operation to rename the output relation. - Assignment(
): - Set Division(
): - Join(
): Similar to Cartesian Product, while satisfying certain situations.- Natural join(
): Natural join between two or more relations will result set of all combination of tuples where they have equal common attribute. - Conditional Join(
): similar to Natural Join with added conditions.

- Theta join: Select rows of a cross product given a certain condition.

- Equijoin: Select rows of a cross product given a equality condition holds between a pair of attributes. - Semi-Join(
) - Outer join
- Left Outer Join(⟕)
- Right Outer Join(⟖)
- Full Outer Join(⟗)

- Natural join(

- Select(
- Logical Operators
- And(
) - Or(
) - Not(
)

- And(

Interactive Graph

Table Of Contents