The GATE Grind

GATE 2025 DA – Question 17

Database Management and Warehousing · Relational algebra, tuple calculus and SQL · 1 mark · Multiple choice

Consider the following three relations:

Car (model, year, serial, color)

Make (maker, model)

Own (owner, serial)

A tuple in Car represents a specific car of a given model, made in a given year, with a serial number and a color. A tuple in Make specifies that a maker company makes cars of a certain model. A tuple in Own specifies that an owner owns the car with a given serial number. Keys are underlined; (owner, serial) together form key for Own. ($\bowtie$ denotes natural join)

$$\pi_{owner}\left(Own \bowtie \left(\sigma_{color = \text{"red"}}\left(Car \bowtie \left(\sigma_{maker = \text{"ABC"}}Make\right)\right)\right)\right)$$

Which one of the following options describes what the above expression computes?

  1. All owners of a red car, a car made by ABC, or a red car made by ABC
  2. All owners of more than one car, where at least one car is red and made by ABC
  3. All owners of a red car made by ABC
  4. All red cars made by ABC

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) All owners of a red car made by ABC

Explanation

Working from the inside, $\sigma_{maker = "ABC"}Make$ keeps the models made by ABC. Joining it with Car on the model gives the cars of those models, and selecting $color = "red"$ keeps the red ones. Joining with Own on the serial number gives the owners of those cars, and projecting on owner lists them. So the result is the set of owners of a red car made by ABC.