In relational algebra, applying the PROJECT operation to a relation produces a…

Concept

Projection is a unary relational-algebra operator that retains only a specified subset of the input relation’s attributes. It does not create new attributes.

Under classical set semantics, duplicate projected tuples are removed. Therefore, projection cannot increase either the number of attributes or the number of tuples.

Application

1. Take R(A, B, C) with tuples (1, x, p), (1, x, q), and (2, y, r), and project it on A and B.

2. Keeping only A and B first gives (1, x), (1, x), and (2, y).

3. Removing the duplicate gives {(1, x), (2, y)}. The field count falls from 3 to 2, and the row count falls from 3 to 2; if all projected tuples were distinct, the row count could remain unchanged but still could not increase.

Cross-check and contrast

• “More fields but not more rows” would still require projection to create attributes outside the input schema, which this operator does not do.

• “More rows but not more fields” would still require output cardinality greater than input cardinality, whereas duplicate elimination makes the bound non-increasing.

• “Both more fields and more rows” combines two increases that projection cannot produce.

• “Neither more fields nor more rows” is consistent with both non-increasing bounds.

Result

Hence, the projected relation has neither more fields nor more rows than the original relation.