Consider the following statements, select your best answer.

Question

BlackTom AI · Accepted Answer

Relational algebra operators map relations to relations because of the closure property: every operator in relational algebra accepts relations (sets of tuples) as inputs and yields a relation as output.

1) Relevant knowledge points and concepts
- Relation: a set (or bag) of tuples with a fixed schema (attributes).
- Relational algebra operators: selection (σ), projection (π), union (∪), set difference (−), Cartesian product (×), join, and rename (ρ).
- Closure property: the result of any relational algebra operator is itself a relation, so results can be further inputs to other operators.

2) Step-by-step reasoning
- Start from the definition: operators act on relations. For example take R(A,B) = {(1,2),(3,4)} and S(B,C) = {(2,5)}.
- Apply selection σ_{A>1}(R): evaluate predicate A>1 for each tuple:
  - For (1,2): 1>1 is false → exclude.
  - For (3,4): 3>1 is true → include.
  Result: relation R1 = {(3,4)}.
- Apply projection π_A(R): extract attribute A from each tuple:
  - From (1,2) → 1 ; from (3,4) → 3.
  Result: relation R2 = {(1),(3)}.
- Apply Cartesian product R × S:
  - Combine each tuple of R with each tuple of S → relation of tuples (A,B,B,C) or after proper renaming (A,B,C).
  Result: a relation.

3) Intermediate steps shown above demonstrate each operator produced relations (R1, R2, R×S).

4) Why the correct answer is correct
Each operator’s output is a relation (a set of tuples with attributes), enabling composition of operations. This is the fundamental closure property of relational algebra, so the statement "A relational algebra operator takes relations as input and produces a relation as output." is true.

5) Why other options are incorrect
- Taking constants as input is false: operators require relations; predicates inside operators may use constants, but the operator inputs remain relations.
- Producing constants as output is false: outputs are relations (sets of tuples), not single constant values.
- Both-inputs-constants and inputs-relations-outputs-constants are incorrect variants contradicting closure.

6) Conclusion
The correct option is "A relational algebra operator takes relations as input and produces a relation as output." This matches the provided answer.

Consider the following statements, select your best answer.Single choice

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