Consider the following statements: S1: Natural join outputs all pairs of rows…
Consider the following statements:
S1: Natural join outputs all pairs of rows from the two input relations.
S2: Cartesian product outputs pairs of rows from the two input relations that have the same value on all attributes that have the same name.
Which of the following is CORRECT?
Answer: A. both S1 and S2 are false — ConceptFor relations R and S, the Cartesian product R × S contains every ordered pair formed by taking one tuple from R and one tuple from S. A natural join…
- A.
both S1 and S2 are false
- B.
S1 is true but S2 is false
- C.
both S1 and S2 are true
- D.
S1 is false but S2 is true
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Show answer & explanation
Correct answer: A
Concept
For relations R and S, the Cartesian product R × S contains every ordered pair formed by taking one tuple from R and one tuple from S. A natural join instead keeps only tuple pairs that agree on every common-named attribute, and then merges the duplicate join columns.
Application
Evaluate S1: saying that a natural join returns all row pairs describes a Cartesian product, not a natural join. Therefore S1 is false.
Evaluate S2: equality on all common-named attributes is the matching condition used by a natural join. A Cartesian product applies no such condition, so S2 is false.
The truth-value pair for (S1, S2) is therefore (false, false).
Cross-check
If the relations have common-named attributes, a natural join is a filtered form of the Cartesian product; only when there are no common attributes do the two coincide. Thus the two statements have exchanged the operators’ definitions.
Contrast
The response “S1 is true but S2 is false” assigns the Cartesian-product behavior to the natural join.
The response “both S1 and S2 are true” treats both exchanged definitions as valid.
The response “S1 is false but S2 is true” assigns the natural-join matching condition to the Cartesian product.
Result: both S1 and S2 are false.