**Relational Algebra **is a set of mathematical principles that allow for the manipulation of the contents in a relational table. Relational Algebra is procedural, meaning the SQL that is written will execute in the order that it was written. It is a set at a time process which means that it will process sets of data instead of individual tuples of data.**Relational Calculus** is also a set of mathematical principles that allow for the manipulation of the contents in a relational table. It is a set at a time process which means that it will process sets of data instead of individual tuples of data.However Relational Calculus is a non-procedural process which means that the written SQL does not have to be done in the order it was written.

Relational Algebra has 8 operations it can perform:

SELECT - Yields values for all rows found in a table, can be used to list either all row values or it can yield only those row values that match a specific criteria, and yields a horizontal subset of a table.

PROJECT - Yields all values for selected attributes and yields a vertical subset of a table.

JOIN - Allows the combination of information from two or more tables and allows the use of independent tables linked by common attributes.

INTERSECT - Yields all the rows that appear in both tables.

- Combines all rows from two tables, excluding duplicate rows, but tables must have the same attribute characteristics.

DIFFERENCE - Yields all rows in one table not found in the other table.

CARTESIAN PRODUCT - Yields all possible pairs of rows from two tables.

DIVIDE - Requires the use of one single-column table and one two-column table.

The 5 operations that can create the other operations are: SELECT, PROJECT, , CARTESIAN PRODUCT, and DIFFERENCE.

Relational Calculus has 3 operations it can perform:

SELECT - Is a restrict operation that yields all rows and specified columns based on the level of restrict.

INTERSECT - Yields all rows that appear in both tables.

- Combines all rows from two tables, excluding duplicate rows, but tables must have the same attribute characteristics.