RA2

Consider the following SQL:

SELECT critic_score
FROM rottentomatoes_movie
NATURAL JOIN imdb_to_rottentomatoes
NATURAL JOIN imdb_movie
WHERE imdb_movie.year = '2022';

In the context of the previous schema for the netflix movie review database schema, which of the following Relational Algebra expressions represent the same resultset as the above SQL? (could be more than one)

The schema is included again for convenience.

Question

RA2

Consider the following SQL:

SELECT critic_score
FROM rottentomatoes_movie
  NATURAL JOIN imdb_to_rottentomatoes
  NATURAL JOIN imdb_movie
WHERE imdb_movie.year = '2022';

In the context of the previous schema for the netflix movie review database schema, which of the following Relational Algebra expressions represent the same resultset as the above SQL? (could be more than one)

The schema is included again for convenience.

BlackTom AI · Accepted Answer

The question asks which Relational Algebra expressions represent the same result as the given SQL query:

SELECT critic_score
FROM rottentomatoes_movie
  NATURAL JOIN imdb_to_rottentomatoes
  NATURAL JOIN imdb_movie
WHERE imdb_movie.year = '2022';

Key observations to reason about:
- The SQL uses NATURAL JOINs among rottentomatoes_movie, imdb_to_rottentomatoes, and imdb_movie. A natural join implicitly joins on all common attribute names among the joined relations.
- After joining, it filters for imdb_movie.year = '2022' and then projects only the critic_score attribute.
- In Relational Algebra, the natural join operator can be represented as the join operator with an implicit equality condition on all common attributes. The exact attribute names may differ, but the semantic result is the same as a standard natural join chain.
- The standard RA pattern for such a query is: first join the three relations (in any order, since join is associative and commutative up to the same set of attributes), then apply the selection σ on the year attribute, and finally apply the projection π on critic_score.

Therefore, the canonical equivalent RA expressions could include:
- π_critic_score ( σ_{imdb_movie.year = '2022'} ( rottentomatoes_movie ⋈ imdb_to_rottentomatoes ⋈ imdb_movie ) )
- π_critic_score ( σ_{imdb_movie.year = '2022'} ( (rottentomatoes_movie ⋈ imdb_to_rottentomatoes) ⋈ imdb_movie ) )
- π_critic_score ( σ_{imdb_movie.year = '2022'} ( rottentomatoes_movie ⋈ imdb_to_rottentomatoes ⋈ imdb_movie ) )
- π_critic_score ( σ_{imdb_movie.year = '2022'} ( (rottentomatoes_movie ⋈ imdb_to_rottentomatoes) ⋈ imdb_movie ) )
(Note: any parenthesization that preserves the same join result is equivalent because join is associative; the important points are the natural joins (or their equivalent ⋈ with the appropriate condition), the selection on year, and the projection of critic_score.)

If there were multiple answer options, they would need to satisfy these properties:
- They perform the same natural joins among the three relations (or an equivalent join with the same join conditions).
- They include a selection σ on imdb_movie.year = '2022' (or an equivalent condition referencing the correct attribute names after the joins).
- They project only the critic_score attribute.

Reasoning about incorrect or non-equivalent forms (general guidance, since specific options are missing):
- Any expression that omits the projection π_critic_score would return more than just critic_score, thus not matching the SQL result. 
- Any expression that applies the selection before the join could yield the same result in some systems if the year attribute is not part of the joined relations, but since year is in imdb_movie, applying σ before the join could filter out rows incorrectly if the join condition changes the set of imdb_movie rows; the safe, equivalent design is to apply σ after performing the joins.
- Expressions that use a different join order but ultimately join the same three relations with the same join conditions are generally equivalent due to the associativity of join.
- Expressions using a cross join followed by a selection that does not reflect the exact year predicate would be incorrect.

In summary, the correct RA forms are those that: (1) join rottentomatoes_movie, imdb_to_rottentomatoes, and imdb_movie with natural joins (or equivalent ⋈ with same attribute conditions), (2) filter to imdb_movie.year = '2022', and (3) project critic_score. Any equivalent ordering of these operations that preserves the same final schema and selection predicate is valid.

INFO20003_2025_SM2 Exam: Database Systems (INFO20003_2025_SM2)- Requires Respondus LockDown Browser

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