(i) DML includes a query language based on both relational algebra and tuple…

In relational database theory, a query language for retrieving data can be procedural or non-procedural. Relational algebra is procedural: it specifies both the desired result and an explicit sequence of operations (selection, projection, join, and so on) to obtain it. Relational calculus is non-procedural (declarative); in its tuple-calculus form it specifies only the desired result through a predicate over tuple variables, leaving the retrieval steps unspecified. Codd's theorem establishes that relational algebra and the safe (domain-independent) tuple relational calculus are equivalent in expressive power (relational completeness).

DML's query language is defined on both foundations together, not implementation detail but textbook grounding. A declarative DML statement, such as SQL's SELECT with a WHERE condition, is a predicate over the desired tuples, which is precisely the tuple-relational-calculus formulation. The same query can equally be written as a sequence of relational-algebra operations, such as selection, projection, and join, that produces the identical result. Because both formulations exist for the same query language and Codd's theorem shows they are equivalent in expressive power, DML's query language is correctly described as based on both relational algebra and tuple calculus, which is exactly what statement (i) says.

• Statement (ii) keeps only the tuple-calculus half and drops the relational-algebra formulation that the same query language is equally defined by under Codd's equivalence, so it is an incomplete description of DML's basis.

• Statement (iii) keeps only the relational-algebra half and drops the tuple-calculus formulation that the same query language is equally defined by under Codd's equivalence, so it too is an incomplete description.

• Statement (iv) denies both foundations, which contradicts the well-established dual algebra-and-calculus basis of relational query languages.

Because DML's query language genuinely combines both formal foundations rather than only one, statement (i), DML includes a query language based on both relational algebra and tuple calculus, is the correct statement.