Expanding Route Data

Join the routes, airlines, and airports tables to obtain: airline_id, airline_name, airline_country, source_city, source_country, target_city, target_country. Let "cells" be the product between the arity and the cardinality of a table.

Question: What is the total number of cells in the result (rows × columns)?

Question

Expanding Route Data

Join the routes, airlines, and airports tables to obtain: airline_id, airline_name, airline_country, source_city, source_country, target_city, target_country. Let "cells" be the product between the arity and the cardinality of a table.

Question: What is the total number of cells in the result (rows × columns)?

BlackTom AI · Accepted Answer

Start by identifying what the question is asking: compute the total number of cells (rows × columns) in the result of joining three tables (routes, airlines, airports) and selecting specific columns. The phrase "Let 'cells' be the product between the arity and the cardinality of a table" defines a cell as a single value in one column of one row, so to get the total number of cells in the final result you need two things: (1) how many columns are in the final projection, and (2) how many rows result from the join.

First, determine the output schema (the number of columns) after projection. The question lists seven columns to select: airline_id, airline_name, airline_country, source_city, source_country, target_city, target_country. Therefore the final projection has 7 columns, assuming there is exactly one value for each of these attributes per joined row. There is no mention of additional columns being included in the result, so we treat the projection as exactly 7 columns.

Second, determine the number of output rows (cardinality) after the join. This depends on:
- the number of rows in the base tables (arity is the number of columns in a table, cardinality is the number of rows);
- the join keys and join type (likely inner join unless stated otherwise);
- how the three tables relate to each other (foreign key relationships between routes and airlines, and between routes and airports).

In general, the number of resulting rows after joining can be computed if you know the join keys and the matching counts. For example, if you inner-join routes with airlines on airline_id, and routes with airports on source_airport_id and target_airport_id (assuming those are the keys), the row count would depend on how many route rows have matching airline and airport records, and how many matches exist for source/target pairs in the airports table. If a route row references invalid or missing airline or airport records, those rows would be dropped in an inner join, reducing the final cardinality. If there are multiple matches (one-to-many or many-to-many relationships in the join paths), the row count could increase accordingly.

Because the problem statement does not provide the actual base table cardinalities (the number of rows in routes, airlines, and airports) or the exact join keys and constraints, it is not possible to compute a numeric final row count (and thus the total number of cells) from the information given. The calculation requires concrete counts for:
- cardinalities of routes, airlines, and airports (or at least the relevant joined cardinalities after applying keys), and
- the exact join conditions (which keys are matched and whether there are one-to-many relationships).

If you had those numbers, the steps would be:
- Compute the resulting row count after performing the joins (inner join by default) using the relevant keys and join logic, taking into account potential one-to-many relationships.
- Multiply that row count by 7 (the number of projected columns) to obtain the total number of cells.

Given only the projection (7 columns) and no base-table counts or join details, there is insufficient information to verify a numeric answer such as 465,829. To proceed, you would need the cardinalities of the base tables or the cardinality of the joined result. If you provide those counts or the table schemas with keys and sample data, I can walk through the exact calculation and confirm the total number of cells.

ECON3310001.1251 Midterm Exam II

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