Final answer:
The extended operators of relational algebra are operations that are not part of the basic set of operators. The outer join operator is an example of an extended operator, while duplicate elimination, cross product, and grouping operators are all basic operators of relational algebra.
Step-by-step explanation:
The extended operators of relational algebra are operations that are not part of the basic set of operators, but are widely used in practice to perform more complex queries and transformations on relational databases.
The outer join operator is an example of an extended operator in relational algebra. It allows us to combine rows from two tables even if there is no match between the values in the join columns.
The other options listed - duplicate elimination, cross product, and grouping operators - are all basic operators of relational algebra. Duplicate elimination removes duplicate rows from a table, cross product combines each row from one table with every row from another table, and grouping operators group rows based on a common attribute or set of attributes.