GATE CS 2022 Set 1 — Question 25
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Databases → Relational Model → Division
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Question
Consider the following three relations in a relational database.Which of the following relational algebra expressions return the set of who own all the brands?
Correct answer
(A) _(eId)(_(eId, bId)(Own) / _(bId)(Brand)); (B) _(eId)(Own) - _(eId)((_(eId)(Own) × _(bId)(Brand)) - _(eId, bId)(Own))
Solution
The query asks for the division operation .
1.Option (A) represents the division operation directly: . This is correct.
2.Option (B) represents the expansion of the division operation using basic operators:
This logic finds all potential (eId, bId) pairs, subtracts actual owned pairs to find missing pairs, projects to find eIds with missing brands, and subtracts those from the set of all eIds. This is the standard definition of division. This is correct.3.Option (C) divides by , which is the set of brands owned by someone, not necessarily all brands in the
Brand table. Incorrect.4.Option (D) is syntactically and logically incorrect.
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