In relational algebra, what does the PROJECT operation produce in terms of the resulting table's columns and rows?

Introduction / Context:
The PROJECT operation in relational algebra selects a subset of columns (attributes) from a relation (table). It is fundamental to query formulation and column pruning for performance. Understanding its exact effect on schema and cardinality avoids misconceptions when translating algebra to SQL (SELECT with specific columns).

Given Data / Assumptions:

• PROJECT removes columns not listed in the projection.
• Duplicates may be eliminated in strict relational algebra (set semantics).
• The operation cannot add new columns or increase row count beyond set semantics.

Concept / Approach:

PROJECT yields fewer or equal columns (never more). Row count is less than or equal to the original, because duplicate rows (after column reduction) can collapse into one. Therefore, options claiming more fields or more rows are incorrect. Likewise, returning all fields of the master table contradicts the definition of projection unless the projection includes all columns, which is not implied here. Hence, ‘‘None of the above’’ is the correct choice among the listed statements.

Step-by-Step Solution:

Verification / Alternative check:

Translating to SQL: SELECT DISTINCT col1, col2 FROM T mirrors set-based project semantics, supporting the reasoning.

Why Other Options Are Wrong:

More fields: Projection prunes columns; cannot create more.

More rows: Projection cannot increase rows; duplicates may reduce them.

All fields: That is not a projection unless explicitly all columns are selected.

Common Pitfalls:

Confusing PROJECT with SELECT (row filtering) or JOIN; projection is column-oriented.

Final Answer:

None of the above