Which relational algebra operation selects tuples that satisfy a given predicate or condition?
The Selection operation (denoted by lowercase Greek letter $\sigma \sigma ) acts as a filter$ that keeps only those tuples that satisfy a specified qualifying condition.
Which relational algebra operation performs a horizontal subsetting of a relation?
Selection extracts specific rows (tuples) based on a condition, which corresponds to horizontal partitioning or subsetting of a table.
Which relational algebra operation extracts specified columns (attributes) from a relation and discards all other columns?
The Projection operation (denoted by pi $\pi ) chooses specified columns$ from a relation, performing vertical slicing and automatically eliminating duplicate tuples in pure relational algebra.
In pure mathematical relational algebra, what happens to duplicate tuples after a Projection ($\pi ) operation$?
Because a mathematical relation is strictly defined as a set of distinct tuples, duplicate rows resulting from projection are automatically discarded.
Which set of relational algebra operations forms a fundamental (basic) set from which other relational operations can be derived?
The five fundamental operations of relational algebra are Selection, Projection, Union, Set Difference, and Cartesian Product. Rename (ρ) is also often added, but other operations like Join, Intersection, and Division are derived.