RA 1

Consider the following problem statement:

List the names of IMDB movies which have a classification of 'pg', or have a director of 'quentin tarantino'.

Which of the following relational algebra expressions correspond to this problem statement? (could be more than one)

The schema is included again for convenience.

Question

RA 1

Consider the following problem statement:

List the names of IMDB movies which have a classification of 'pg', or have a director of 'quentin tarantino'.

Which of the following relational algebra expressions correspond to this problem statement? (could be more than one)

The schema is included again for convenience.

BlackTom AI · Accepted Answer

To tackle this question, I’ll break down what each candidate relational-algebra expression is doing and whether it matches the problem statement.

Option 1: π_title(σ_classification="pg"(imdb_movie)) ∪ π_title(σ_name="quentin tarantino"(imdb_movie ⨝ imdb_movie.lead_director=imdb_person.id imdb_person))
- The left part, π_title(σ_classification="pg"(imdb_movie)), selects the titles of all movies whose classification is pg directly from imdb_movie. This captures all pg movies.
- The right part performs a join between imdb_movie and imdb_person on imdb_movie.lead_director = imdb_person.id, then selects rows where imdb_person.name = "quentin tarantino", and finally projects the title. This yields all movies whose director is Quentin Tarantino.
- The union of these two projections gives the set of titles that are either pg-rated or directed by Tarantino (with duplicates removed by the relational-algebra semantics). This aligns with the problem statement, which asks for names of IMDB movies with classification pg OR with a director Tarantino.
- Potential subtlety: the first part does not require any join, while the second part relies on the join to access the director’s name. Both parts are correctly formed and then united.

Option 2: π_title(σ_classification="pg" OR name="quentin tarantino"(imdb_movie ⨝ imdb_movie.lead_director=imdb_person.id imdb_person))
- This expression first performs a join between imdb_movie and imdb_person using the same lead_director-to-id condition.
- Then it applies a single selection with the predicate (classification = 'pg' OR name = 'quentin tarantino'). That means any tuple in the joined relation is kept if either its classification is pg or its director’s name is Tarantino.
- After that, it projects only the title.
- Semantically, this should produce the same result as Option 1, since it captures the union of the two conditions within one selection instead of two separate steps. However, a potential pitfall could be operator precedence or scoping in some presentation conventions, but in standard relational algebra the OR within the selection on the joined relation is acceptable and yields the same set of titles as the union approach.

Summary of correctness considerations for both options:
- Both expressions utilize the same underlying join between imdb_movie and imdb_person to access director names, which is necessary for Tarantino-centered filtering.
- Both expressions target the correct fields: pg classification from imdb_movie and director name from imdb_person.
- Both ultimately project the title, returning movie names only, which matches the problem’s request.
- The two expressions are logically equivalent under standard relational-algebra semantics (one uses union of two selective steps; the other uses a single selective step with an OR predicate after the join).

Therefore, both options appear to conform to the problem statement, each implementing the intended set of movie titles via slightly different but equivalent relational-algebra constructions.

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

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